Linear Unbiased Estimator Research Articles

Assessing genetic diversity and aggregate genotype selection in a collection of cumin (Cuminum cyminum L.) accessions under drought stress: Application of BLUP and BLUE

Maintaining genetic diversity and aggregate traits selection in medicinal plants improves selection efficiency and provides the flexibility to adapt environmental stresses. The present studies aimed at evaluating genetic variation and assessing efficiency of three selection index models based on relative economic values of traits and a ranking based method in 30 cumin accessions under drought and well-watered conditions in 2015 and 2016 years. Drought stress regime applied at the flowering stage of growth cycle. The best linear unbiased estimation values (BLUE) were used for aggregate genotype selection in a desired direction in the Smith-Hazel I (SMH-I) and II (SMH-II), and Pesek-Baker (PSB) indices. The three selection indices did differ in assigning relative economic values for traits tested in cumin. Best linear unbiased predictions (BLUP) were used to predict rank summation index values (RSI). Grain yield (GY) ranged from 183.07 to 379.99 kg/ha and from 430.07 to 942.26 kg/ha in 2015 and 2016 experiments, respectively. Of the accessions tested in 2015, 20 with top rankings for GY were selected for further validation in 2016. Selections in 2015 resulted in 7.1% for plant height (PH) to 165.7% for plant weight (PW) progress in drought treatment in 2016. Among the traits, PH, thousand grain weight (TGW) and harvest index (HI) showed low changes between the two moisture regimes. Plant height with high heritability and significant correlation with GY showed low variation over seasons and watering regime treatments and is suggested for indirect selection of GY. Analysis of drought susceptibility index (DSI) showed that Kashmar with low DSI had low genotype × environment interaction for GY. Grains per plant (GPP) and biological yield traits had the highest response to selection under drought stress. The SMH-II showed higher selection efficiency in both seasons. Zarand had top rankings for RSI among accessions for aggregate traits tested under drought conditions in both years. Our results showed aggregate genotype selection is a refinement of selection which incorporates information of individual genotypes with genetic and association of traits. Overall, the efficiency of SMH II which maximized genetic gains in a desired direction was higher than SMH I and PSB indices that helps to achieve breeding goals in an uncertain number of generations in cumin.

New improved Poisson and negative binomial item count techniques for eliciting truthful answers to sensitive questions

Abstract Item count techniques (ICTs) are indirect survey questioning methods designed to deal with sensitive features. These techniques have gained the support of many applied researchers and undergone further theoretical development. Latterly in the literature, two new item count methods, called Poisson and negative binomial ICTs, have been proposed. However, if the population parameters of the control variable are not provided by the outside source, the methods are not very efficient. Efficiency is an important issue in indirect methods of questioning due to the fact that the protection of respondents’ privacy is usually achieved at the expense of the efficiency of the estimation. In the present paper we propose new improved Poisson and negative binomial ICTs, in which two control variables are used in both groups, although in a different manner. In the paper we analyse best linear unbiased and maximum likelihood estimators of the proportion of the sensitive attribute in the population in the introduced new models. The theoretical findings presented in the paper are supported by a comprehensive simulation study. The improved procedure allowed the increase of the efficiency of the estimation compared to the original Poisson and negative binomial ICTs.

Optimal designs for some bivariate cokriging models

This article focuses on the estimation and design aspects of a bivariate collocated cokriging experiment. For a large class of covariance matrices, a linear dependency criterion is identified, which allows the best linear unbiased estimator of the primary variable in a bivariate collocated cokriging setup to reduce to a univariate kriging estimator. Exact optimal designs for efficient prediction for such simple and ordinary reduced cokriging models with one-dimensional inputs are determined. Designs are found by minimizing the maximum and the integrated prediction variance, where the primary variable is an Ornstein–Uhlenbeck process. For simple and ordinary cokriging models with known covariance parameters, the equispaced design is shown to be optimal for both criterion functions. The more realistic scenario of unknown covariance parameters is addressed by assuming prior distributions on the parameter vector, thus adopting a Bayesian approach to the design problem. The equispaced design is proved to be the Bayesian optimal design for both criteria. The work is motivated by designing an optimal water monitoring system for an Indian river.

Improved Shape Parameter Estimation for the Three-Parameter Log-Logistic Distribution

The log-logistic distribution is widely used in different fields of study such as survival analysis, hydrology, insurance, and economics. Recently, Ahsanullah and Alzaatreh studied the best linear unbiased estimators for the location and the scale parameters of the three-parameter log-logistic model. The same authors also propose a shift-invariant Hill estimator for the unknown shape parameter. In this work, we propose a new estimation method for the shape parameter. We derive its nondegenerate asymptotic behaviour and analyse its finite sample performance through a Monte Carlo simulation study. To have precise estimates, we present a method for selecting the threshold. To illustrate the improvement achieved, efficiency comparisons are also provided.

A comprehensive framework for assessing the accuracy and uncertainty of global above-ground biomass maps

Over the past decade, several global maps of above-ground biomass (AGB) have been produced, but they exhibit significant differences that reduce their value for climate and carbon cycle modelling, and also for national estimates of forest carbon stocks and their changes. The number of such maps is anticipated to increase because of new satellite missions dedicated to measuring AGB. Objective and consistent methods to estimate the accuracy and uncertainty of AGB maps are therefore urgently needed. This paper develops and demonstrates a framework aimed at achieving this. The framework provides a means to compare AGB maps with AGB estimates from a global collection of National Forest Inventories and research plots that accounts for the uncertainty of plot AGB errors. This uncertainty depends strongly on plot size, and is dominated by the combined errors from tree measurements and allometric models (inter-quartile range of their standard deviation (SD) = 30–151 Mg ha−1). Estimates of sampling errors are also important, especially in the most common case where plots are smaller than map pixels (SD = 16–44 Mg ha−1). Plot uncertainty estimates are used to calculate the minimum-variance linear unbiased estimates of the mean forest AGB when averaged to 0.1∘. These are used to assess four AGB maps: Baccini (2000), GEOCARBON (2008), GlobBiomass (2010) and CCI Biomass (2017). Map bias, estimated using the differences between the plot and 0.1∘ map averages, is modelled using random forest regression driven by variables shown to affect the map estimates. The bias model is particularly sensitive to the map estimate of AGB and tree cover, and exhibits strong regional biases. Variograms indicate that AGB map errors have map-specific spatial correlation up to a range of 50–104 km, which increases the variance of spatially aggregated AGB map estimates compared to when pixel errors are independent. After bias adjustment, total pantropical AGB and its associated SD are derived for the four map epochs. This total becomes closer to the value estimated by the Forest Resources Assessment after every epoch and shows a similar decrease. The framework is applicable to both local and global-scale analysis, and is available at https://github.com/arnanaraza/PlotToMap. Our study therefore constitutes a major step towards improved AGB map validation and improvement.

Faktor yang Mempengaruhi Return Saham dengan Harga Saham sebagai Variabel Moderasi (Studi Kasus pada Perusahan Perbankan yang Terdaftar di BEI)

This study aims to know the factors that impact stock return with Market Price as the moderating variable of the banking company listed on the IDX from 2015 to 2020. The data is retrieved from idx.co.id. The population of this article is 43 banking companies, and to select the sample for this article has used purposive sampling and has selected 11 companies. The analysis method of this article has used descriptive statistics. The data has gone through BLUE (best linear unbiased estimator) test, such as normality test, autocorrelation test, multicollinearity test, and heteroscedasticity test before doing the hypothesis test. Further, the analysis data has used F-test, t-test, the equation of multiple linear regression, determination coefficient, and moderation. The study's findings are that, partially, LDR does not affect SR, ROA does not affect SR, and BOPO does not affect SR. PBV can not moderate the effect of LDR, ROA, and BOPO on stock return. The determination coefficient is 0.048 (4.8%), which means that the LDR, ROA, and BOPO have impacted SR as much as 4.8%, and the remaining is affected by other factors. The contribution of the research is to help the investors select the right stock.

A sensor data fusion algorithm based on suboptimal network powered deep learning

To improve the performance of data fusion in wireless sensor networks, based on the suboptimal network powered deep learning model, a data fusion algorithm that combines a stacked autoencoder (SAE) and a clustering protocol is proposed. The fusion algorithm for sensor data is investigated by suboptimal network powered deep learning to analyse the fusion processing at the sensor measurement level and the fusion processing at the localization result level. This paper establishes a suboptimal network powered deep learning model and derives its weighted least squares solution algorithm based on this model, also, the best linear unbiased estimation method for fusion of vibration sensor and vision sensor localization results is adopted. First, to overcome the filter divergence caused by rounding error, reduce the computational complexity, ensure the non-negativity of the covariance, and improve the convergence speed of the filter, the target state volume after fusion using the proposed model is closer to the real state volume of the target compared to the state volume of each local sensor detection, verify the validity of the algorithm was increased.

Estimation of a Linear Model in Terms of Intra-Class Correlations of the Residual Error and the Regressors

Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.

A Remote Estimation Method of Smart Meter Errors Based on Neural Network Filter and Generalized Damping Recursive Least Square

To solve large-scale smart meter verification and periodic replacement problems, a remote estimation method based on neural network filter (NNF) and generalized damping recursive least square (GDRLS) is proposed. In this article, a smart meter error estimation model with a loss noise filter is built. A typical loss noise filter is designed with a neural network, so that the filtered loss noise meets the Gauss–Markov condition, which paves the way for the best linear unbiased estimation (BLUE). GDRLS algorithm is applied to solve the novel estimation model, which can effectively address the problem that large loss estimation errors merge small smart meter errors. Then, a complete process of the proposed method is constructed, which can estimate both the user smart meter errors, and the loss noises accurately. Finally, the effectiveness, superiority, and applicability of the proposed method are verified through simulation analysis and practical distribution network application.

The Effect of COVID-19 Pandemic on Corporate Dividend Policy in Indonesia: The Static and Dynamic Panel Data Approaches

This research examines the effect of the crisis due to the COVID-19 pandemic on dividend policy in Indonesia. The purposive sampling method was used to collect data from corporates listed on the IDX from 2014 to 2020 and analyzed using static and dynamic panel data approaches. The fixed-effect models (FEM) were selected for the static panel data regression. Meanwhile, the first difference-generalized method of moments (FD-GMM) and system-generalized method of moments (SYS-GMM) were used for determine the robustness of the estimated dynamic panel data. The results showed that the crisis due to the pandemic led to higher dividend distribution on SYS-GMM. Furthermore, companies maintained the dividend level as a positive signal for investors which lifted the sluggish trade condition in the capital market. Profitability and previous year dividends positively affect dividend policy robustly. Furthermore, the results showed that age affects dividend policy on FD-GMM. Financial leverage has a robust effect, and firm size has an effect on FD-GMM in different directions, while investment opportunity does not affect dividend policy. Statistically, the FEM selected that violates the best linear unbiased estimation was proven to form parameters that were not much different from the estimates produced by the dynamic model, both from the coefficient of influence direction and significance, and the omitted variable bias occurs as evidenced in the robust test with dynamic model was solved. This research is also used as a reference for considering investors’ investment decisions in the new normal condition. Therefore, dividend policy can be considered as a positive signal to investors with the ability to stock trading activities in the capital market.

Efficient Generalized Ridge Regression

Abstract The original ridge estimator of the unknown p×1 vector of β-coefficients in a linear model used a single scalar, k, to determine a point on a shrinkage path of finite length that extends from the Ordinary Least Squares estimator, ^β 0, to the shrinkage terminus (usually ^β ≡ 0). Generalized ridge estimators use two or more parameters to determine not only the shape of their shrinkage path but also a specific point on that path. The efficient generalized ridge regression path proposed here is a continuous two-piece linear function that (1) starts at ^β 0, the Best Linear Unbiased Estimator, (2) has its interior knot at the ^ β-estimator with Maximum Likelihood of achieving overall minimum MSE risk under normal distribution-theory, and (3) ends at the shrinkage terminus. This new path is efficient in the senses that it is the shortest path and, at least when p > 2, essentially the only known shrinkage path that always contains the ^ β-vector that is most likely to be optimally biased. Functions in R-packages freely distributed via CRAN perform the calculations and produce the graphics used here to illustrate shrinkage concepts by interpreting ridge Trace diagnostic plots. These new concepts and visual tools provide invaluable data-analytic insights and improved self-confidence to applied researchers and data scientists fitting linear models when p, the number of non-constant X-predictor variables in the model, is strictly less than the number of observations available.

Conservative Linear Unbiased Estimation Under Partially Known Covariances

Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible to maintain full knowledge about the correlations. One example is decentralized data fusion where the cross-correlations between estimates are unknown, partly due to information sharing. To avoid underestimating the covariance of an estimate in such situations, conservative estimation is one option. In this paper the conservative linear unbiased estimator is formalized including optimality criteria. Fundamental bounds of the optimal conservative linear unbiased estimator are derived. A main contribution is a general approach for computing the proposed estimator based on robust optimization. Furthermore, it is shown that several existing estimation algorithms are special cases of the optimal conservative linear unbiased estimator. An evaluation verifies the theoretical considerations and shows that the optimization based approach performs better than existing conservative estimation methods in certain cases.

Kriging Model for Reliability Analysis of the Offshore Steel Trestle Subjected to Wave and Current Loads

Offshore steel trestles (OSTs) are exposed to severe marine environments with stochastic wave and current loads, making structural safety assessment challenging and difficult. Reliability analysis is a suitable way to consider both wave and current loading intensity uncertainties, but the implicit and complex limit state functions of the reliability analysis usually imply huge computational costs. This paper proposes an efficient reliability analysis framework for OST using the kriging model of optimal linear unbiased estimation. The surrogate model is built with stochastic waves, current parameters, and the corresponding load factors. The framework is then used to evaluate the reliability of an example OST subjected to wave and current loads at three limit states of OST, including first yield (FY), full plastic (FP), and collapse initiation (CI). Three different distributions are used for comparison of the results of failure probability and reliability index. The results and the computational cost by the proposed framework are compared with that from the Monte Carlo sampling (MCS) and Latin hypercube sampling (LHS) method. The influences of sample number on the prediction accuracy and reliability index are investigated. The influence of marine growth on the reliability analysis of the OST is discussed using MCS and the kriging model. The results show that the reliability analysis based on the kriging model can obtain the reliability index for the OST efficiently with less calculation time but similar results compared with MCS and LHS. With the increase of the number of samples, the prediction accuracy of the kriging model increases, and the corresponding failure probability fluctuates greatly at first and then tends to be stable. The reliability of the example OST is reduced with the increase of marine growth, regardless of the limit state.

Improvement of Multi-GNSS Precision and Success Rate Using Realistic Stochastic Model of Observations

With the advancement of multi-constellation and multi-frequency global navigation satellite systems (GNSSs), more observations are available for high precision positioning applications. Although there is a lot of progress in the GNSS world, achieving realistic precision of the solution (neither too optimistic nor too pessimistic) is still an open problem. Weighting among different GNSS systems requires a realistic stochastic model for all observations to achieve the best linear unbiased estimation (BLUE) of unknown parameters in multi-GNSS data processing mode. In addition, the correct integer ambiguity resolution (IAR) becomes crucial in shortening the Time-To-Fix (TTF) in RTK, especially in challenging environmental conditions. In general, it is required to estimate various variances for observation types, consider the correlation between different observables, and compensate for the satellite elevation dependence of the observable precision. Quality control of GNSS signals, such as GPS, GLONASS, Galileo, and BeiDou can be performed by processing a zero or short baseline double difference pseudorange and carrier phase observations using the least-squares variance component estimation (LS-VCE). The efficacy of this method is investigated using real multi-GNSS data sets collected by the Trimble NETR9, SEPT POLARX5, and LEICA GR30 receivers. The results show that the standard deviation of observations depends on the system and the observable type in which a particular receiver could have the best performance. We also note that the estimated variances and correlations among different observations are also dependent on the receiver type. It is because the approaches utilized for the recovery techniques differ from one type of receiver to another kind. The reliability of IAR will improve if a realistic stochastic model is applied in single or multi-GNSS data processing. According to the results, for the data sets considered, a realistic stochastic model can increase the computed empirical success rate to 100% in multi-GNSS as well as a single system. As mentioned previously, the realistic precision of the solution can be achieved with a realistic stochastic model. However, using the estimated stochastic model, in fact, leads to better precision and accuracy for the estimated baseline components, up to 39% in multi-GNSS.

A multi-method forecasting algorithm: Linear unbiased estimation of combine forecast

This paper proposes a dynamic ensemble algorithm to combine forecasting results from multiple methodologies subject to their local (recent) predictive performance. In contrast to conventional combination forecasts, the proposed algorithm runs a sparsification process to merge a subset of methodology space to avoid overfitting and improve out-of-sample accuracy. The methodology space consists of various linear and non-linear as well as univariate and multivariate forecasting algorithms frequently used in the literature and industrial practice. The proposed algorithm continuously searches for the best combination to learn models weight. The weights are then used to combine the next forecasting coming from all forecasters. Two empirical studies are presented for illustrating its mechanism and predictive performance: crude oil price forecasting problem and tourist arrival forecasting. Empirical results support the fact that there is no one-fits-all methodology that outperforms in all periods. Our combination algorithm picks a different subset in each step, so the combination structure is dynamically redefined. Although some methodologies perform poorly, and they are never selected for the subset (e.g., ARIMA, ETS), most other methodologies are interchangeably picked or discarded from the combination structure.

Production and Profitability of Hybrid Rice Is Influenced by Different Nutrient Management Practices

The government of Nepal has recommended blanket fertilizer application for rice cultivation, which results in lower nutrient use efficiency (NUE) particularly under rainfed conditions. With the aim of finding an appropriate nutrient management practices concerning rice production and profitability, a field experiment was conducted during rainy season of 2017 and 2018 at Kavrepalanchowk and Dang district of Nepal. Altogether, five treatments comprising various nutrient management practices viz. Nutrient Expert Model (NE), use of Leaf Color Chart (LCC), Government Recommended Fertilizer Dose (GON), Farm Yard Manure (FYM), and Farmers’ Field Practice (FFP), were laid out in RCBD with four replications in farmers’ fields. The analysis of variance showed significant difference between treatments for test weight and grain yield in Kavrepalanchowk whereas all traits except number of effective tillers were significant in Dang. The significantly higher grain yield and harvest index were obtained in NE, followed by LCC; and the overall straw yield was highest in LCC, followed by NE in both the locations. Also, yield gap analysis suggested the NE had 44.44% and 23.97% increase in yield as compared to FPP in Kavrepalanchowk and Dang, respectively. The combined analysis with Best Linear Unbiased Estimator revealed the interaction of nutrient management and location significantly effects the straw yield and harvest index across both the locations. The estimated mean straw yield and harvest index were 10.93 t/ha and 34.98%, respectively. Both correlation study and biplot of principal component analysis signaled grain yield had positive correlation with all other traits. Furthermore, the net revenue was maximum for NE, followed by LCC in both the locations. The benefit: cost ratio was highest for NE which was 1.55 in Kavrepalanchowk and 2.61 in Dang. On the basis of these findings, NE and LCC can be effectively used as nutrient management practice by the farmers to obtain maximum production and profitability in Rice.

Genomic Selection and Genome-Wide Association Studies for Grain Protein Content Stability in a Nested Association Mapping Population of Wheat

Grain protein content (GPC) is controlled by complex genetic systems and their interactions and is an important quality determinant for hard spring wheat as it has a positive effect on bread and pasta quality. GPC is variable among genotypes and strongly influenced by the environment. Thus, understanding the genetic control of wheat GPC and identifying genotypes with improved stability is an important breeding goal. The objectives of this research were to identify genetic backgrounds with less variation for GPC across environments and identify quantitative trait loci (QTLs) controlling the stability of GPC. A spring wheat nested association mapping (NAM) population of 650 recombinant inbred lines (RIL) derived from 26 diverse founder parents crossed to one common parent, ‘Berkut’, was phenotyped over three years of field trials (2014–2016). Genomic selection models were developed and compared based on predictions of GPC and GPC stability. After observing variable genetic control of GPC within the NAM population, seven RIL families displaying reduced marker-by-environment interaction were selected based on a stability index derived from a Finlay–Wilkinson regression. A genome-wide association study identified eighteen significant QTLs for GPC stability with a Bonferroni-adjusted p-value < 0.05 using four different models and out of these eighteen QTLs eight were identified by two or more GWAS models simultaneously. This study also demonstrated that genome-wide prediction of GPC with ridge regression best linear unbiased estimates reached up to r = 0.69. Genomic selection can be used to apply selection pressure for GPC and improve genetic gain for GPC.

Plant breeding increases spring wheat yield potential in Afghanistan

AbstractWheat (Triticum aestivum L.) is an essential food security crop in Afghanistan. To determine the contribution of wheat breeding to increasing productivity, we analyzed data obtained from 192 trials conducted over 11 locations from 2002–2003 to 2015–2016. Using this data, we estimated annual genetic gains for grain yield, days to heading and plant height over the 14‐yr period. We used best linear unbiased estimates to measure genetic gains across CIMMYT Elite Spring Wheat Yield Trials per se and for the top 5 and top 10% performing genotypes relative to checks. Mean realized genetic gain for grain yield was 115 kg ha–1 yr−1, whereas the top 10 genotypes achieved annual yield gains of 123 kg ha–1. The continually replaced local checks also contributed an annual genetic gain for yield of 107 kg ha–1. The associated adaptive traits days to heading and plant height varied in their response over time with the top 10 yielding genotypes having a 1.82 d annual reduction in heading date while plant height increased by 0.77 cm yr−1 for the same set of genotypes. Results show that continual breeding improvements confer yield gains, contributing to increasing Afghan wheat productivity. This has wider relevance for demonstrating the value of continued investment in public sector plant breeding supporting wheat production and food security in Central Asia.

Optimal Designs for Comparing Regression Curves: Dependence Within and Between Groups

We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to derive efficient designs we use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in a corresponding continuous model. It is demonstrated that in general simultaneous estimation using the data from both groups yields more precise results than estimation of the parameters separately in the two groups. Using the BLUE from simultaneous estimation, we then construct an efficient linear estimator for finite sample size by minimizing the mean squared error between the optimal solution in the continuous model and its discrete approximation with respect to the weights (of the linear estimator). Finally, the optimal design points are determined by minimizing the maximal width of a simultaneous confidence band for the difference of the two regression functions. The advantages of the new approach are illustrated by means of a simulation study, where it is shown that the use of the optimal designs yields substantially narrower confidence bands than the application of uniform designs.

Statistical modelling of rate gyros based on fully overlapping Allan variance

Angular random walk and rate random walk are two dominant random noise components which are inherent in almost gyroscopes. Therefore, modelling these noise components accurately is very important. Here, a modified algorithm is proposed for estimating the two random noise components accurately. Up to now, the statistical modelling of the two random noise components has been conducted by the best linear unbiased estimator, which is based on the formulae for mean, variance and covariance of non-overlapping Allan variance of them, that is, angular random walk and rate random walk. The modified algorithm is developed by using the best linear unbiased estimator, based on formulae for mean, variance and covariance of fully-overlapping Allan variance which are newly derived in this paper. Efficiency of the algorithm is evaluated by simulation and experiment.