Use Of Auxiliary Information Research Articles

On Effective Dual Use of Auxiliary Information in Variability Control Charts

During the last decade, variance control charts based on different sampling schemes have attracted research interest in the field of statistical process control. These charts used extra (auxiliary) information either for ranking of units or estimation rather than using it for both. The effectiveness of a control chart can be increased by utilizing the auxiliary information for dual purposes. This article is focused on developing a generalized structure of variance control charts based on dual use of auxiliary information under different sampling strategies and runs rules. The generalized structure mainly depends on three auxiliary information-based estimators with dual use of auxiliary information, three bivariate process distributions, and variety of sampling schemes. The performance of the proposed control charts is investigated by assessing the power curve. We have observed that the proposals of the study perform better than its complement. An application example is also provided for practitioners' concerns to monitor the stability of physicochemical parameter of groundwater. Copyright © 2015 John Wiley & Sons, Ltd.

On Dual Use of Auxiliary Information for Efficient Monitoring

In this study, a new idea has been proposed in statistical process control by making dual use of auxiliary information, that is, for ranking as well as at the estimation stage. The control charts are proposed based on regression estimator in three basic ranked set schemes, that is, ranked-set sampling (RSS), median RSS, and extreme RSS. The power of detection is used as a performance measure for evaluation and comparison of control charts. Comparisons revealed that the newly proposed charts (making dual use of auxiliary information) performed significantly better compared with the existing location charts. An illustrative example is also provided for the application of the proposed charts. Copyright © 2015 John Wiley & Sons, Ltd.

Empirical likelihood for semivarying coefficient model with measurement error in the nonparametric part

A semivarying coefficient model with measurement error in the nonparametric part was proposed by Feng and Xue (Ann Inst Stat Math 66:121–140, 2014), but its inferences have not been systematically studied. This paper applies empirical likelihood method to construct confidence regions/intervals for the regression parameter and coefficient function. When some auxiliary information about the parametric part is available, the empirical log-likelihood ratio statistic for the regression parameter is introduced based on the corrected local linear estimator of the coefficient function. Furthermore, corrected empirical log-likelihood ratio statistic for coefficient function is also investigated with the use of auxiliary information. The limiting distributions of the resulting statistics both for the regression parameter and coefficient function are shown to have standard Chi-squared distribution. Simulation experiments and a real data set are presented to evaluate the finite sample performance of our proposed method.

Efficient Use of Auxiliary Information in Estimating the Population Ratio, Product and Mean in Presence of Non-Response

Efficient Use of Auxiliary Information in Estimating the Population Ratio, Product and Mean in Presence of Non-Response

A new exponential ratio-type estimator with linear combination of two auxiliary variables.

In sample surveys, it is usual to make use of auxiliary information to increase the precision of estimators. We propose a new exponential ratio-type estimator of a finite population mean using linear combination of two auxiliary variables and obtain mean square error (MSE) equation for proposed estimator. We find theoretical conditions that make proposed estimator more efficient than traditional multivariate ratio estimator using information of two auxiliary variables, the estimator of Bahl and Tuteja and the estimator proposed by Abu-Dayeh et al. In addition, we support these theoretical results with the aid of two numerical examples.

CHAIN REGRESSION-TYPE ESTIMATOR USING MULTIPLE AUXILIARY INFORMATION IN SUCCESSIVE SAMPLING

Housila P. Singh, Manoj Kumar Srivastava, Namita Srivastava, Tanveer A. Tarray, Virendra Singh, and Shivam Dixit ∗ Abstract In successive sampling, the use of auxiliary information for estimation of population mean on current occasion is a well explored area. In the present work, the information on an auxiliary variable, which is available on both the occasions, is used along with the information on the study variable from the previous occasion and the current occasion. Consequently, chain regression-type estimator for estimating the population mean are proposed in two occasions successive sampling. The optimal replacement policy is also discussed. We have also given an empirical study along with pictorial representation to examine the merit of the proposed estimator.

Estimation of Mode Using Two-phase Sampling

In this article, we consider the problem of estimation of mode using two-phase sampling. Ratio- and difference-type estimators in two-phase sampling are proposed. The asymptotic properties of the proposed estimators are studied analytically as well as empirically for different situations for the given cost of surveys. The use of two-phase sampling has been found to be cost saving design while estimating mode by making a proper use of auxiliary information.

Determining [formula omitted] optimum calibration points to construct calibration estimators of the distribution function

Survey statisticians make use of auxiliary information to improve estimates, for example in calibration estimation, introduced in Deville and Särndal (1992), which is used to obtain new weights that are close to the basic design weights and that, at the same time, comply with benchmark constraints on the auxiliary information available. Rueda et al. (2007) applied this calibration technique to estimate the distribution function. This estimator of the distribution function is built by means of constraints that require the use of a set of fixed values t1,t2,…,tP. The precision of the resulting calibration estimator varies according to the selection of ti. In the present work, we study the problem of determining the optimal values ti that give the best possible estimation under simple random sampling without replacement.

Estimation of Mode Using Auxiliary Information

In this article, we propose naïve estimator, ratio estimator, and difference estimator of the mode of a study variable by using the known mode of an auxiliary variable. The asymptotic properties of the proposed estimators are studied analytically as well as empirically for different situations. The proper use of auxiliary information is found to result in efficient ratio and difference estimators than the naïve estimator.

A Survey of Molecular Descriptors Used in Mass Spectrometry Based Proteomics

The field of proteomics has grown vertiginously in the last years. This has been due fundamentally to technological improvements in the instrumentation, methods, and easy-to-use software, thereby making it possible to address a large number of biological questions and to deepen the study of the proteome of several organisms. The development in the field has imposed a challenge in the computational analysis of the commonly obtained large datasets generated in a single proteomics experiment, which still remains. An alternative to tackle this general issue has been the use of auxiliary information generated during the proteomics experiment to validate the confidence of the identifications. In this manuscript we review the main molecular descriptors used for building predictor models for estimating retention time, isoelectric point and peptide "detectability", which are key tools in the design of several validation strategies based in these criteria. We also give an overview of the main open source tools and libraries used for computing molecular descriptors.

On Improving Ratio/Product Estimator by Ratio/Product-cum-Mean-per-Unit Estimator Targeting More Efficient Use of Auxiliary Information

To achieve a more efficient use of auxiliary information we propose single-parameter ratio/product-cum-mean-per-unit estimators for a finite population mean in a simple random sample without replacement when the magnitude of the correlation coefficient is not very high (less than or equal to 0.7). The first order large sample approximation to the bias and the mean square error of our proposed estimators are obtained. We use simulation to compare our estimators with the well-known sample mean, ratio, and product estimators, as well as the classical linear regression estimator for efficient use of auxiliary information. The results are conforming to our motivating aim behind our proposition.

Empirical Likelihood for Estimating Equations with Nonignorably Missing Data.

We develop an empirical likelihood (EL) inference on parameters in generalized estimating equations with nonignorably missing response data. We consider an exponential tilting model for the nonignorably missing mechanism, and propose modified estimating equations by imputing missing data through a kernel regression method. We establish some asymptotic properties of the EL estimators of the unknown parameters under different scenarios. With the use of auxiliary information, the EL estimators are statistically more efficient. Simulation studies are used to assess the finite sample performance of our proposed EL estimators. We apply our EL estimators to investigate a data set on earnings obtained from the New York Social Indicators Survey.

The Chain Ratio Estimator and Regression Estimator with Linear Combination of Two Auxiliary Variables

In sample surveys, it is usual to make use of auxiliary information to increase the precision of the estimators. We propose a new chain ratio estimator and regression estimator of a finite population mean using linear combination of two auxiliary variables and obtain the mean squared error (MSE) equations for the proposed estimators. We find theoretical conditions that make proposed estimators more efficient than the traditional multivariate ratio estimator and the regression estimator using information of two auxiliary variables.

On efficient use of auxiliary information for control charting in SPC

In Statistical Process Control (SPC), monitoring of the process dispersion has a major impact on the performance of processes like manufacturing, management and services. Control charts act as the most important SPC tool, used to differentiate between common and special cause variations in the process. The use of auxiliary information can enhance the detection ability of control charts and hence an efficient monitoring of process parameter(s) can be done. This study deals with the Shewhart type variability control charts based on auxiliary characteristics for the non-cascading processes, assuming stability of auxiliary parameters. The control chart structures of these variability charts are provided and their performance evaluations are carried out in terms of average run length (ARL), relative average run length (RARL) and extra quadratic loss (EQL) under the normal and t distributed process environments. The comparisons have been made among different variability charts and superiorities are established based on their detection abilities for different amounts of shifts in process dispersion. An illustrative example is also provided in support of the theory, and finally the study ends with concluding remarks and suggestions for future research.

Estimation of soil organic matter by geostatistical methods: Use of auxiliary information in agricultural and environmental assessment

Mapping soil properties such as soil organic matter (SOM), or soil organic carbon (SOC) content represent a problem often arising in agronomic and environmental surveys, since point data must be spatialized with the best interpolation. Deterministic methods (Inverse Distance Weighting, Splines, ecc.) do not account for the error, thus probabilistic methods as geostatistics (e.g. Ordinary Kriging, OK) have been successfully applied for many years. Maps derived from this kind of stochastic interpolation, based only on a recognized autocorrelation among measured points, could not be suitable in representing the reality, since they usually show a smoothed pattern. Hybrid interpolation methods, such as Regression Kriging (RK), combine an interpolation based only on point data and an interpolation based on a regression of the target variable with other continuous variables, spatially related, well known on the whole area.In the Teramo province, central Italy, a set of 250 soil samples, collected from the surface horizon of agricultural soils is available. From these samples the estimation of soil texture, SOC, SOM related to texture and C/N both by OK and RK was performed. The following predictors were used for RK: (i) indexes derived from Landsat TM imagery, (ii) morphometric parameters derived from DEM, (iii) soil subsystems map 1:250,000. The maps obtained by both OK and RK in this survey show substantial agreement, without significant improvement in map accuracy using auxiliary information.

Empirical likelihood inference for mean functionals with nonignorably missing response data

An empirical likelihood (EL) approach to inference on mean functionals with nonignorably missing response data is developed. The nonignorably missing mechanism is specified by an exponential tilting model. Several maximum EL estimators (MELEs) for the response mean functional are proposed under different scenarios. We systematically investigate asymptotic properties of the proposed MELEs for the response mean functional. With the use of auxiliary information, MELEs are statistically more efficient. Confidence intervals (CIs) for the response mean are constructed on the basis of the EL method and the normal approximation (NA) method. Simulation studies are presented to evaluate the finite sample performance of our proposed MELEs and CIs. A real earnings data from the New York Social Indicators Survey is used to illustrate our proposed EL method. Empirical results show that our proposed EL method is robust.

ON THE USE OF AUXILIARY INFORMATION IN MULTIPURP OSE ROTATING SURVEYS

In most repeated surveys interest centers both on the estimation of the pop ulation mean on each successive occasion and estimation of further population parameters like net c hanges, number index estimation or average over several occasions. Due to this fact many of repeate d surveys are rotating surveys. The multipurpose nature of repeated surveys poses additional questions to the already difficult theory of rotating surveys. The aim of the paper is to analyze how the use of auxiliary information on each successive occasion and consequently increase of the ef ficiency of the mean estimation on each rotating surveys.occasion affects efficiency of net changes estimation in tthe case of repeated

Robust Lavallée-Hidiroglou stratified sampling strategy

There are several reasons why robust regression techniques are useful tools in sampling design. First of all, when stratified samples are considered, one needs to deal with three main issues: the sample size, the strata bounds determination and the sample allocation in the strata. Since the target variable Y, the objective of the survey, is unknown, some auxiliary information X known for the entire population from which the sample is drawn, is used. Such information is helpful as it is typically strongly correlated with the target Y. However, some discrepancies between these variables may arise. The use of auxiliary information, combined with the choice of the appropriate statistical model to estimate the relationship between Y and X, is crucial for the determination of the strata bounds, the size of the sample and the sampling rates according to a chosen precision level for the estimates, as has been shown by Rivest (2002). Nevertheless, this regression-based approach is highly sensitive to the presence of contaminated data. Since the key tool for stratified sampling is the measure of scale of Y conditional on the knowledge of the auxiliary X, a robust approach based on the S-estimator of the regression is proposed in this paper. The aim is to allow for robust sample size and strata bounds determination, together with optimal sample allocation. Simulation results based on data from the Construction sector of a Structural Business Survey illustrate the advantages of the proposed method.

Undiagnosed HIV prevalence in France

Supervie and Costagliola [1] comments suggest first that our conclusion is not in accordance with our analysis. Our estimated 0.09% undiagnosed HIV prevalence is below the 0.10% threshold suggested by health authorities for implementing universal screening. We agree that this difference is not statistically significant. However, that value, obtained in the most affected area in France, combined with the fact that undiagnosed infections were only found in high-risk groups,’ amply justifies our conclusion that a ‘universal testing strategy should be questioned in France’. A second remark states that, in a previous study [2], we claimed that the Emergency Department (ED) tested population was representative of the French population. That is a misinterpretation. We clearly mentioned that those two populations differed by over-representations of foreign-born people (particularly sub-Saharan Africans), women with more than 1 sexual partner during the last 12 months and more frequent HIV screening among the ED-tested population (see Table 1, p. 14) [2]. Thus, ED-undiagnosed HIV prevalence could not be considered the same as that of the general population. That situation then led us to estimate the general population prevalence with a calibration method [3]. Such a method is not applied to reduce bias in the sampling frame, as Supervie and Costagliola [1] claim, but to decrease the variance of estimators through the use of auxiliary information, which could not initially be taken into account in the design of the survey [4]. Our analysis used sociodemographic data, for example, sex and age from a population census, to perform a poststratification (also called standardization) and included data on sexual orientation and country of birth, which could not be crossed with all the other variables, and thus required a raking ratio method [5].Table 1: Characteristics of patients HIV tested in Emergency Departments and completing questionnaires compared with a reference general population.We thank Supervie and Costagliola [1] for giving us the opportunity to provide more details on the calibration method used, which, along with the management of missing data through multiple imputations allowed us to obtain an accurate and reliable estimate of the undiagnosed-HIV prevalence in the general population. Acknowledgements Conflicts of interest Dr A-C.C. reports receiving grants from Janssen–Cilag, Novartis, AstraZeneca, Aventis and Haeraus for consultancies, workshops and travel to meetings and accommodations. Dr P. de T. reports receiving grants from Abbott, BMS, Gilead, MSD, Tibotec Janssen and ViiV Healthcare for workshops and travel to meetings and accommodations. Dr F.S. reports receiving grants for the evaluation of Orasure RTD. The other authors have no disclosures to declare.

Tensor factorization using auxiliary information

Most of the existing analysis methods for tensors (or multi-way arrays) only assume that tensors to be completed are of low rank. However, for example, when they are applied to tensor completion problems, their prediction accuracy tends to be significantly worse when only a limited number of entries are observed. In this paper, we propose to use relationships among data as auxiliary information in addition to the low-rank assumption to improve the quality of tensor decomposition. We introduce two regularization approaches using graph Laplacians induced from the relationships, one for moderately sparse cases and the other for extremely sparse cases. We also give present two kinds of iterative algorithms for approximate solutions: one based on an EM-like algorithms which is stable but not so scalable, and the other based on gradient-based optimization which is applicable to large scale datasets. Numerical experiments on tensor completion using synthetic and benchmark datasets show that the use of auxiliary information improves completion accuracy over the existing methods based only on the low-rank assumption, especially when observations are sparse.