Linear Prediction Estimates Research Articles

Exploring the Foreign Language Book Borrowing Habits of University Instructors and Prospective Teachers (2012–2022)

Understanding the widespread adoption of foreign language books (FLBs) is imperative for language learners and educators, as it facilitates evaluating the efficacy and caliber of language resources. Using MARC-based bibliography analysis, the researcher uncovers publishing and subject information of popular FLBs and utilizes survival analysis to calculate the FLBs’ survival index. After conducting factor analysis, the researcher applies linear regression prediction and Bayesian estimation to determine the total number of FLB borrowings and borrowers. The borrowing index of FLBs collected in the past five years surpasses that of books collected for more than five years, and staff members demonstrate higher borrowing activity compared to undergraduate students, postgraduate students, and other readers. Acceptance emerges as the most critical factor influencing the total number of FLB borrowings and borrowers, cultural dominance has a relatively minor impact, and personal background is found to be less negatively influential. The estimates of the total number of FLB borrowers indicate that acceptance is constrained by personal background, which is restricted by cultural dominance.

Genome-wide association studies for a comprehensive understanding of the genetic architecture of culm strength and yield traits in rice.

Lodging resistance in rice is a complex trait determined by culm morphological and culm physical strength traits, and these traits are a major determinant of yield. We made a detailed analysis of various component traits with the aim of deriving optimized parameters for measuring culm strength. Genotyping by sequencing (GBS)-based genome-wide association study (GWAS) was employed among 181 genotypes for dissecting the genetic control of culm strength traits. The VanRaden kinship algorithm using 6,822 filtered single-nucleotide polymorphisms (SNPs) revealed the presence of two sub-groups within the association panel with kinship values concentrated at<0.5 level, indicating greater diversity among the genotypes. A wide range of phenotypic variation and high heritability for culm strength and yield traits were observed over two seasons, as reflected in best linear unbiased prediction (BLUP) estimates. The multi-locus model for GWAS resulted in the identification of 15 highly significant associations (p< 0.0001) for culm strength traits. Two novel major effect marker-trait associations (MTAs) for section modulus and bending stress were identified on chromosomes 2 and 12 with a phenotypic variance of 21.87% and 10.14%, respectively. Other MTAs were also noted in the vicinity of previously reported putative candidate genes for lodging resistance, providing an opportunity for further research on the biochemical basis of culm strength. The quantitative trait locus (QTL) hotspot identified on chromosome 12 with the synergistic association for culm strength trait (section modulus, bending stress, and internode breaking weight) and grain number can be considered a novel genomic region that can serve a dual purpose of enhancing culm strength and grain yield. Elite donors in the indica background with beneficial alleles of the identified major QTLs could be a valuable resource with greater significance in practical plant breeding programs focusing on improving lodging resistance in rice.

Packet Loss Compensation for VoIP through Bone‐Conducted Speech Using Modified Linear Prediction

In this paper, we compare air‐conducted (AC) speech with bone‐conducted (BC) speech for the purpose of utilizing them in packet loss concealment (PLC) for speech quality of voice over internet protocol (VoIP). Instead of the autocorrelation method of linear prediction (LP), which was utilized in the conventional PLC techniques, we employ the modified covariance (MC) method. The MC method provides accurate LP estimation from short input data samples and avoids the numerical problem the autocorrelation method suffers from. The lost frame is compensated from both forward and backward directions in which linear gain and weighting are applied. When BC speech is used as the input speech data for PLC in the case where the speech sender is in noisy environments, BC speech behaves more accurately than the corresponding AC speech, resulting in an excellent performance of the LP‐based PLC technique. This unveils a useful use of BC speech in speech information systems. Experiments show that in severe noise environments of AC speech‐to‐noise ratio being less than 10 dB, BC speech is superior to AC speech for PLC. It is also shown that the transmitted BC speech is more accurately reconstructed for PLC than transmitted AC speech is done. © 2023 The Authors. IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Performance of copula and nested error regression models in estimating per capita expenditure of sub-district in Pidie Regency

In unit-level small area estimation (SAE), the commonly used nested error regression (NER) model assumes normality which is not always the case. To handle non-normal data, researchers in statistics have developed a novel approach using exchangeable and extendible copula called the multivariate exchangeable copula (MEC) model. This study compares the performance of parametric MEC and NER models in estimating the sub-district average of per capita expenditure (PCE) in Pidie Regency, Aceh Province. This study presents PCE, which has a skewed distribution of the three-parameter skew-normal. The parametric MEC model uses a Gaussian copula from the Elliptical family and an empirical best unbiased prediction (EBUP) estimator. Meanwhile, the NER model uses an empirical best linear unbiased prediction (EBLUP) estimator. The results reveal that at a 95% confidence level, the parametric MEC model outperforms the NER model with a smaller root of mean squared error (RMSE) and provides a more precise estimate of the sub-district average of PCE. This study highlights the importance of considering the parametric MEC model as an alternative method for skewed data in unit-level SAE. The results of this study have the potential to support the achievement of Goal 1 (to end poverty) and Goal 10 (to reduce inequality) of the sustainable development goals (SDGs) by providing average PCE estimates at the sub-district level.

Impact of genomic preselection on subsequent ssGBLUP evaluation of preselected animals for scarcely recorded feed intake in pigs.

We have previously shown that single-step genomic best linear unbiased prediction (ssGBLUP) estimates breeding values of genomically preselected animals without preselection bias for widely recorded traits, that is traits recorded for the majority of animals in the breeding population. This study investigated the impact of genomic preselection (GPS) on accuracy and bias in ssGBLUP evaluation of genomically preselected animals for a scarcely recorded trait, that is a trait recorded for only a small proportion of the animals, which generally has a lower prediction accuracy than widely recorded traits, mainly due to having a much smaller number of phenotypes available. We used data from a commercial pig breeding program, considering feed intake as a scarcely recorded target trait, being available for ~30% of the animals with phenotypes for any trait, and average daily gain, backfat thickness and loin depth as widely recorded predictor traits, being available for >95% of the animals with phenotypes for any trait. The data contained the routine GPS implemented by commercial animal breeding programs, and we retrospectively implemented two scenarios with additional layers of GPS by discarding pedigree, genotypes and phenotypes of animals without progeny. The ssGBLUP evaluation following GPS used records only from the target trait, only from the predictor traits, or both. Accuracy for feed intake did not differ statistically across GPS scenarios, although it tended to decrease with more intense GPS. The accuracy had average values of 0.37, 0.44, and 0.45 across all GPS scenarios when, respectively, records from only the target trait, only the predictor traits, or both were used in the ssGBLUP evaluation. Considerable deflation of the genomic breeding values for feed intake was observed in the most stringent GPS scenario, due to the variance components being underestimated as a result of the limited amount of strongly preselected data. As long as (co)variance components were unbiased, no or only marginal bias was observed. These results for accuracy and bias were observed whether records of the scarcely recorded target trait, of the predictor traits, or both were used in the ssGBLUP evaluation. Our results show that for the scarcely recorded feed intake in pigs, ssGBLUP is able to estimate breeding values of preselected animals without preselection bias, similarly as previously observed for widely recorded traits.

Cross-trait prediction accuracy of summary statistics in genome-wide association studies.

In the era of big data, univariate models have widely been used as a workhorse tool for quickly producing marginal estimators; and this is true even when in a high-dimensional dense setting, in which many features are "true," but weak signals. Genome-wide association studies (GWAS) epitomize this type of setting. Although the GWAS marginal estimator is popular, it has long been criticized for ignoring the correlation structure of genetic variants (i.e., the linkage disequilibrium [LD] pattern). In this paper, we study the effects of LD pattern on the GWAS marginal estimator and investigate whether or not additionally accounting for the LD can improve the prediction accuracy of complex traits. We consider a general high-dimensional dense setting for GWAS and study a class of ridge-type estimators, including the popular marginal estimator and the best linear unbiased prediction (BLUP) estimator as two special cases. We show that the performance of GWAS marginal estimator depends on the LD pattern through the first three moments of its eigenvalue distribution. Furthermore, we uncover that the relative performance of GWAS marginal and BLUP estimators highly depends on the ratio of GWAS sample size over the number of genetic variants. Particularly, our finding reveals that the marginal estimator can easily become near-optimal within this class when the sample size is relatively small, even though it ignores the LD pattern. On the other hand, BLUP estimator has substantially better performance than the marginal estimator as the sample size increases toward the number of genetic variants, which is typically in millions. Therefore, adjusting for the LD (such as in the BLUP) is most needed when GWAS sample size is large. We illustrate the importance of our results by using the simulated data and realGWAS.

Increased Azimuth Resolution by Extrapolating the Antenna Array Aperture Function by Least Squares Linear Prediction Estimation Using Autoregressive Model Coefficients

Introduction. Short-wave stations for detecting airborne objects of the ionospheric type have a number of limited technical characteristics, one of which is their low azimuth resolution. This limitation is manifested in the impossibility to separately observe air objects in a group, the distance between which is less than 30 km (at an observation range of 2000 km). The technical characteristics under consideration can be improved by making changes to the dimensions of the receiving antenna array (AA); however, such changes lead, as a rule, to unjustified engineering and financial costs. In practice, space-time signal processing is carried out using conventional superresolution methods, which, although increasing the resolution of the station, decrease the rate of delivery of observation results to the operator due to an additional computational load. It is necessary to find a compromise between the maximum possible resolution indicator and the acceptable load on the system during signal processing.Aim. Analysis of the phase distribution of the incident wave scattered by objects at the AA aperture, as well as the azimuthal images of these objects when performing spacetime signal processing after extrapolating the AA aperture function by evaluating linear prediction using the least-squares method using autoregressive model coefficients.Materials and methods. Modelling of phase distributions at the AA aperture and azimuthal images of the observed objects was conducted in the MATLAB environment.Results. It is shown that the problem of increasing the azimuth resolution of a short-wave station for detecting air objects can be successfully solved using linear prediction based on the least-squares method using autoregressive model coefficients for the extrapolation of the AA aperture function. The results obtained during modelling were analysed using the example of group observation of air objects.Conclusion. The proposed approach for extrapolation of the AA aperture function for short-wave stations with large receiving AAs proved its relevance. The method proposed for increasing the resolution is characterized by a lower computational load, thereby being promising for practical application.

The comparative study of three nonparametric methods of SAR tomography for building reconstruction

Over the past years, synthetic aperture radar (SAR) tomography (TomoSAR) has indicated significant potentials for three-dimensional (3D) reconstruction of buildings in urban areas. A large number of SAR images are thus required to perform tomographic inversions in non-parametric spectral estimators. To this end, in the case of a limited choice of SAR acquisitions, the present study aims to evaluate the capabilities of five non-parametric spectral estimation (SE) techniques, including linear prediction (LP), maximum entropy (ME), and minimum norm (MN), Capon, and beamforming (BF) in the tomographic reconstruction of urban environments. The performance analysis is carried out by using both simulated and real SAR datasets. The study results demonstrate that the proposed efficient LP estimator, minimizing the average output signal power over the antenna array elements, can separate the layover scatterers along the height direction. This low-computational SE method is thus able to clean side lobes while using a small number of observations. The proposed algorithms, as applied on TerraSAR-X strip-map images of the city of Tehran, Iran, verify the effectiveness of the non-parametric LP reconstruction technique for urban buildings. The estimated height of the scatterers also indicates that the LP estimator is similar to the field-based measurements once compared with ME, MN, Capon, and BF reconstruction methods.

Hierarchical Bayesian Small Area Estimation Using Weakly Informative Priors in Ecologically Homogeneous Areas of the Interior Western Forests

The U.S. Forest Inventory and Analysis Program (FIA) collects inventory data on and computes estimates for many forest attributes to monitor the status and trends of the nation's forests. Increasingly, FIA needs to produce estimates in small geographic and temporal regions. In this application, we implement area level hierarchical Bayesian (HB) small area estimators of several forest attributes for ecosubsections in the Interior West of the US. We use a remotely-sensed auxiliary variable, percent tree canopy cover, to predict response variables derived from ground-collected data such as basal area, biomass, tree count, and volume. We implement four area level HB estimators that borrow strength across ecological provinces and sections and consider prior information on the between-area variation of the response variables. We compare the performance of these HB estimators to the area level empirical best linear unbiased prediction (EBLUP) estimator and to the industry-standard post-stratified (PS) direct estimator. Results suggest that when borrowing strength to areas which are believed to be homogeneous (such as the ecosection level) and a weakly informative prior distribution is placed on the between-area variation parameter, we can reduce variance substantially compared the analogous EBLUP estimator and the PS estimator. Explorations of bias introduced with the HB estimators through comparison with the PS estimator indicates little to no addition of bias. These results illustrate the applicability and benefit of performing small area estimation of forest attributes in a HB framework, as they allow for more precise inference at the ecosubsection level.

A class of general adjusted maximum likelihood methods for desirable mean squared error estimation of EBLUP under the Fay–Herriot small area model

The empirical best linear unbiased prediction (EBLUP) estimator is utilized for efficient inference in various research areas, especially for small-area estimation. In order to measure its uncertainty, we generally need to estimate its mean squared prediction error (MSE). Ideally, an EBLUP-based method should not only provide a second-order unbiased estimator of MSE of EBLUP but also maintain strict positivity in estimators of both model variance parameter and MSE of EBLUP. Fortunately, the MSE estimators proposed in Yoshimori and Lahiri (2014) and Hirose and Lahiri (2018) achieve the three desired properties simultaneously. As far as we know, no other MSE estimator does so.In this paper, we therefore seek an adequate class of general adjusted maximum-likelihood methods that simultaneously achieve the three desired properties of MSE estimation. To establish that the investigated class does so, we reveal the relationship between the general adjusted maximum-likelihood method for the model variance parameter and the general functional form of the second-order unbiased MSE estimator, maintaining strict positivity. We also compare the performance of several MSE estimators in our investigated class and others through a Monte Carlo simulation study. The results show that the MSE estimators in our investigated class perform better than those in others.

The Linear Predictive Modeling of Speech From Higher-Lag Autocorrelation Coefficients Applied to Noise-Robust Speaker Recognition

A linear predictive spectral estimation method based on higher-lag autocorrelation coefficients is proposed for the noise-robust feature extraction from speech. The method, called higher-lag linear prediction, is derived from a signal prediction model that is optimized in the mean square sense using a cost function that has two prediction error terms, the first of which is similar to that of conventional linear prediction and the second of which is a delayed version introducing an integer delay of M samples. This basic form is developed further into the combined higher-lag linear prediction (CHLLP) model by simultaneously taking advantage of the zero-lag and higher-lag predictions. The CHLLP model was used in the computation of mel-frequency cepstral coefficients and compared with several reference feature extraction methods in speaker recognition. The experiments were conducted by using a modern i-vector-based system. Noise-corruption was done using both additive car, babble, and factory noise in different signal-to-noise ratio conditions as well as speech recordings from real noisy conditions. The results indicate that CHLLP outperformed the reference feature extraction methods in almost all the comparisons in the noise-corrupted conditions and the performance of CHLLP was only slightly inferior to the nonparametric FFT-based spectral modeling in the clean condition.

Estimates of genetic parameters and genetic gains for growth traits of two Eucalyptus urophylla populations in Zululand, South Africa

In South Africa, Eucalyptus urophylla is an important species due to its disease tolerance to fungal diseases such as Crysoporthe austroafricana and the Coniothyrium sp. cankers. It is mainly planted as a parental species in a hybrid combination with E. grandis. Generally, the E. grandis × E. urophylla hybrid has better disease tolerance and higher wood density than pure E. grandis. The current strategy is to maintain large breeding populations of both parental species in order to provide improved elite selections for hybrid crosses on a regular basis. With this in mind, two E. urophylla populations, consisting of five provenance/progeny trials, were established in the subtropical region of Zululand. The aims of this study were, firstly, to determine the magnitude of genotype × environment interaction of E. urophylla in Zululand; secondly, to estimate genetic parameters and correlations for diameter at breast height (DBH), height and volume; and thirdly, to identify selections to advance the current breeding population as well as to hybridise with E. grandis. Results indicated that genotype × environment interaction effects would be practically negligible for growth in Zululand and therefore a single breeding population will be appropriate. In general, all growth traits were under low to moderate genetic control, with narrow-sense heritabilities ranging between 0.14 and 0.48 for volume. The genetic correlations between growth traits were high (0.98 and 0.99 for DBH– volume). This is an indication that DBH is a sufficient growth measure to use in E. urophylla breeding programmes. Best linear unbiased prediction estimates indicated that aa selection scenario of 200 individuals will generate genetic gains of 44.7% over the population mean. The estimated gains for the top 50 individuals that could potentially be used as hybrid parents to cross with E. grandis was 59.8% over the population mean.

Fusion estimation using measured outputs with random parameter matrices subject to random delays and packet dropouts

This paper investigates the centralized and distributed fusion estimation problems for discrete-time random signals from multi-sensor noisy measurements, perturbed by random parameter matrices, which are transmitted to local processors through different communication channel links. It is assumed that both one-step delays and packet dropouts can randomly occur during the data transmission, and different white sequences of Bernoulli random variables with known probabilities are introduced to depict the transmission delays and losses at each sensor. Using only covariance information, without requiring the evolution model of the signal process, a recursive algorithm for the centralized least-squares linear prediction and filtering estimators is derived by an innovation approach. Also, local least-squares linear estimators based on the measurements received by the processor of each sensor are obtained, and the distributed fusion method is then used to generate fusion predictors and filters by a matrix-weighted linear combination of the local estimators, using the mean squared error as optimality criterion. In order to compare the performance of the centralized and distributed fusion estimators, recursive formulas for the estimation error covariance matrices are also derived. A numerical example illustrates how some usual network-induced uncertainties can be dealt with the current observation model with random matrices.

Statistical properties of linear prediction analysis underlying the challenge of formant bandwidth estimation.

Formant bandwidth estimation is often observed to be more challenging than the estimation of formant center frequencies due to the presence of multiple glottal pulses within a period and short closed-phase durations. This study explores inherently different statistical properties between linear prediction (LP)-based estimates of formant frequencies and their corresponding bandwidths that may be explained in part by the statistical bounds on the variances of estimated LP coefficients. A theoretical analysis of the Cramér-Rao bounds on LP estimator variance indicates that the accuracy of bandwidth estimation is approximately twice as low as that of center frequency estimation. Monte Carlo simulations of all-pole vowels with stochastic and mixed-source excitation demonstrate that the distributions of estimated LP coefficients exhibit expectedly different variances for each coefficient. Transforming the LP coefficients to formant parameters results in variances of bandwidth estimates being typically larger than the variances of respective center frequency estimates, depending on vowel type and fundamental frequency. These results provide additional evidence underlying the challenge of formant bandwidth estimation due to inherent statistical properties of LP-based speech analysis.

On small area estimation under a sub-area level model

We propose an extension of the well-known Fay and Herriot (1979) area level model to sub-area level. Not only this model may be used to estimate small area means by borrowing strength from related areas, but also by borrowing strength from sub-areas to obtain more efficient sub-area estimators. Model-based empirical best linear unbiased prediction (EBLUP) estimators are obtained from the BLUP estimators by replacing the model parameters by suitable estimators, using an iterative method based on weighted residual sum of squares. Second order approximations to the mean squared error (MSE) of the EBLUP estimators are obtained and then used to drive MSE estimators unbiased to second order. Results of simulation studies on the performance of the proposed estimators are also provided.

A new adjusted maximum likelihood method for the Fay–Herriot small area model

In the context of the Fay–Herriot model, a mixed regression model routinely used to combine information from various sources in small area estimation, certain adjustments to a standard likelihood (e.g., profile, residual, etc.) have been recently proposed in order to produce strictly positive and consistent model variance estimators. These adjustments protect the resulting empirical best linear unbiased prediction (EBLUP) estimator of a small area mean from the possible over-shrinking to the regression estimator. However, in certain cases, the existing adjusted likelihood methods can lead to high biases in the estimation of both model variance and the associated shrinkage factors and can even produce a negative second-order unbiased mean square error (MSE) estimate of an EBLUP. In this paper, we propose a new adjustment factor that rectifies the above-mentioned problems associated with the existing adjusted likelihood methods. In particular, we show that our proposed adjusted residual maximum likelihood and profile maximum likelihood estimators of the model variance and the shrinkage factors enjoy the same higher-order asymptotic bias properties of the corresponding residual maximum likelihood and profile maximum likelihood estimators, respectively. We compare performances of the proposed method with the existing methods using Monte Carlo simulations.

Small area estimation of forest attributes in the Norwegian National Forest Inventory

The Norwegian National Forest Inventory (NNFI) provides estimates of forest parameters on national and regional scales by means of a systematic network of permanent sample plots. One of the biggest challenges for the NNFI is the interest in forest attribute information for small sub-populations such as municipalities or protected areas. Frequently, too few sampled observations are available for such small areas to allow estimates with acceptable precision. However, if an auxiliary variable exists that is correlated with the variable of interest, small area estimation (SAE) techniques may provide means to improve the precision of estimates. The study aimed at estimating the mean above-ground forest biomass for small areas with high precision and accuracy, using SAE techniques. For this purpose, the simple random sampling (SRS) estimator, the generalized regression (GREG) estimator, and the unit-level empirical best linear unbiased prediction (EBLUP) estimator were compared. Mean canopy height obtained from a photogrammetric canopy height model (CHM) was the auxiliary variable available for every population element. The small areas were 14 municipalities within a 2,184 km2 study area for which an estimate of the mean forest biomass was sought. The municipalities were between 31 and 527 km2 and contained 1–35 NNFI sample plots located within forest. The mean canopy height obtained from the CHM was found to have a strong linear correlation with forest biomass. Both the SRS estimator and the GREG estimator result in unstable estimates if they are based on too few observations. Although this is not the case for the EBLUP estimator, the estimators were only compared for municipalities with more than five sample plots. The SRS resulted in the highest standard errors in all municipalities. Whereas the GREG and EBLUP standard errors were similar for small areas with many sample plots, the EBLUP standard error was usually smaller than the GREG standard error. The difference between the EBLUP and GREG standard error increased with a decreasing number of sample plots within the small area. The EBLUP estimates of mean forest biomass within the municipalities ranged between 95.01 and 153.76 Mg ha−1, with standard errors between 8.20 and 12.84 Mg ha−1.

Estimating speech spectra for copy synthesis by linear prediction and by hand

Linear prediction is a widely available technique for analyzing acoustic properties of speech, although this method is known to be error-prone. New tests assessed the adequacy of linear prediction estimates by using this method to derive synthesis parameters and testing the intelligibility of the synthetic speech that results. Matched sets of sine-wave sentences were created, one set using uncorrected linear prediction estimates of natural sentences, the other using estimates made by hand. Phoneme restrictions imposed on linguistic properties allowed comparisons between continuous and intermittent voicing, oral or nasal and fricative manner, and unrestricted phonemic variation. Intelligibility tests revealed uniformly good performance with sentences created by hand-estimation and a minimal decrease in intelligibility with estimation by linear prediction due to manner variation with continuous voicing. Poorer performance was observed when linear prediction estimates were used to produce synthetic versions of phonemically unrestricted sentences, but no similar decline was observed with synthetic sentences produced by hand estimation. The results show a substantial intelligibility cost of reliance on uncorrected linear prediction estimates when phonemic variation approaches natural incidence.

Mean squared error estimators of small area means using survey weights

Using survey weights, You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] proposed a pseudo-empirical best linear unbiased prediction (pseudo-EBLUP) estimator of a small area mean under a nested error linear regression model. This estimator borrows strength across areas through a linking model, and makes use of survey weights to ensure design consistency and preserve benchmarking property in the sense that the estimators add up to a reliable direct estimator of the mean of a large area covering the small areas. In this article, a second-order approximation to the mean squared error (MSE) of the pseudo-EBLUP estimator of a small area mean is derived. Using this approximation, an estimator of MSE that is nearly unbiased is derived; the MSE estimator of You & Rao [You and Rao, The Canadian Journal of Statistics 2002; 30, 431–439] ignored cross-product terms in the MSE and hence it is biased. Empirical results on the performance of the proposed MSE estimator are also presented. The Canadian Journal of Statistics 38: 598–608; 2010 © 2010 Statistical Society of Canada En utilisant les poids d'échantillonnage, You et Rao (You et Rao, La revue canadienne de statistique, 2002; 30; 431-439) ont proposé l'utilisation du meilleur prédicteur linéaire sans biais pseudo-empirique (pseudo-EBLUP) pour l'estimation des moyennes de petits domaines sous un modèle de régression linéaire emboîtée. Cet estimateur utilise l'information des autres domaines via un modèle de couplage et il utilise les poids d'échantillonnage afin de s'assurer de la cohérence par rapport au plan d'échantillonnage et de sauvegarder sa calibration, c'est-à-dire que la somme des estimateurs conduit directement à un estimateur fiable de la moyenne d'une grande région recouvrant les petits domaines. Dans cet article, une approximation du second ordre de l'erreur quadratique moyenne (MSE) de l'estimateur pseudo-EBLUP pour la moyenne des petits domaines est obtenue. En utilisant cette approximation, nous obtenons un estimateur du MSE qui est presque sans biais, celui proposé dans You et Rao (You et Rao, La revue canadienne de statistique, 2002; 30; 431-439) ignore les termes croisés dans le MSE et par conséquent, il est biaisé. Des résultats empiriques sur la performance de l'estimateur du MSE proposé dans cet article sont aussi présentés. La revue canadienne de statistique 38: 598–608; 2010 © 2010 Société statistique du Canada

Robust small area estimation

AbstractSmall area estimation has received considerable attention in recent years because of growing demand for small area statistics. Basic area‐level and unit‐level models have been studied in the literature to obtain empirical best linear unbiased prediction (EBLUP) estimators of small area means. Although this classical method is useful for estimating the small area means efficiently under normality assumptions, it can be highly influenced by the presence of outliers in the data. In this article, the authors investigate the robustness properties of the classical estimators and propose a resistant method for small area estimation, which is useful for downweighting any influential observations in the data when estimating the model parameters. To estimate the mean squared errors of the robust estimators of small area means, a parametric bootstrap method is adopted here, which is applicable to models with block diagonal covariance structures. Simulations are carried out to study the behaviour of the proposed robust estimators in the presence of outliers, and these estimators are also compared to the EBLUP estimators. Performance of the bootstrap mean squared error estimator is also investigated in the simulation study. The proposed robust method is also applied to some real data to estimate crop areas for counties in Iowa, using farm‐interview data on crop areas and LANDSAT satellite data as auxiliary information. The Canadian Journal of Statistics 37: 381–399; 2009 © 2009 Statistical Society of Canada