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Journal articles on the topic 'Best linear unbiased estimator'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Štulajter, František. "Robustness of the best linear unbiased estimator and predictor in linear regression models." Applications of Mathematics 35, no. 2 (1990): 162–68. http://dx.doi.org/10.21136/am.1990.104398.

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2

Sjöberg, Lars. "On the Best Quadratic Minimum Bias Non-Negative Estimator of a Two-Variance Component Model." Journal of Geodetic Science 1, no. 3 (September 1, 2011): 280–85. http://dx.doi.org/10.2478/v10156-011-0006-y.

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On the Best Quadratic Minimum Bias Non-Negative Estimator of a Two-Variance Component ModelVariance components (VCs) in linear adjustment models are usually successfully computed by unbiased estimators. However, for many unbiased VC techniques estimated variance components might be negative, a result that cannot be tolerated by the user. This is, for example, the case with the simple additive VC model aσ2/1 + bσ2/2 with known coefficients a and b, where either of the unbiasedly estimated variance components σ2/1 + σ2/2 may frequently come out negative. This fact calls for so-called non-negative VC estimators. Here the Best Quadratic Minimum Bias Non-negative Estimator (BQMBNE) of a two-variance component model is derived. A special case with independent observations is explicitly presented.

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3

Liu, Yonghui. "On equality of ordinary least squares estimator, best linear unbiased estimator and best linear unbiased predictor in the general linear model." Journal of Statistical Planning and Inference 139, no. 4 (April 2009): 1522–29. http://dx.doi.org/10.1016/j.jspi.2008.08.015.

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4

Wang, Xiang. "A best linear unbiased estimator for multi-seam deposits." International Journal of Mining and Geological Engineering 6, no. 3 (October 1988): 259–66. http://dx.doi.org/10.1007/bf00880977.

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5

Wu, Jibo, and Chaolin Liu. "The best linear unbiased estimator in a singular linear regression model." Statistical Papers 59, no. 3 (July 28, 2016): 1193–204. http://dx.doi.org/10.1007/s00362-016-0811-6.

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6

Puntanen, Simo, George P. H. Styan, and Hans Joachim Werner. "Two matrix-based proofs that the linear estimator Gy is the best linear unbiased estimator." Journal of Statistical Planning and Inference 88, no. 2 (August 2000): 173–79. http://dx.doi.org/10.1016/s0378-3758(00)00076-8.

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7

Mäkinen, J. "A bound for the Euclidean norm of the difference between the best linear unbiased estimator and a linear unbiased estimator." Journal of Geodesy 76, no. 6-7 (July 1, 2002): 317–22. http://dx.doi.org/10.1007/s00190-002-0262-9.

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8

Baksalary, Oskar Maria, and Götz Trenkler. "A projector oriented approach to the best linear unbiased estimator." Statistical Papers 50, no. 4 (August 2009): 721–33. http://dx.doi.org/10.1007/s00362-009-0252-6.

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9

Wu, Jong-Wuu, Sheau-Chiann Chen, Wen-Chuan Lee, and Heng-Yi Lai. "Weighted Moments Estimators of the Parameters for the Extreme Value Distribution Based on the Multiply Type II Censored Sample." Scientific World Journal 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/281624.

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We propose the weighted moments estimators (WMEs) of the location and scale parameters for the extreme value distribution based on the multiply type II censored sample. Simulated mean squared errors (MSEs) of best linear unbiased estimator (BLUE) and exact MSEs of WMEs are compared to study the behavior of different estimation methods. The results show the best estimator among the WMEs and BLUE under different combinations of censoring schemes.

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10

Schaden, Daniel, and Elisabeth Ullmann. "On Multilevel Best Linear Unbiased Estimators." SIAM/ASA Journal on Uncertainty Quantification 8, no. 2 (January 2020): 601–35. http://dx.doi.org/10.1137/19m1263534.

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11

AL-Mouel, Abdulhussein Saber, and Jasim Mohammed Ali. "Best Quadratic unbiased Estimator for Variance Component of One-Way Repeated Measurement Model." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 1 (April 30, 2018): 7615–23. http://dx.doi.org/10.24297/jam.v14i1.7342.

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The studies of analysis of variance components is one of the important topics in mathematical statistics for this subject of wide application. In this paper given best quadratic unbiased estimator of variance components for balanced data for linear one-way repeated measurement model (RMM). We computed the quadratic unbiased estimator, which has minimum variance (best quadratic unbiased estimate (BQUE)) by using analysis of variance (ANOVA) method of estimating the variance components.

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12

Chan, F. K. W., H. C. So, J. Zheng, and K. W. K. Lui. "Best linear unbiased estimator approach for time-of-arrival based localisation." IET Signal Processing 2, no. 2 (2008): 156. http://dx.doi.org/10.1049/iet-spr:20070190.

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13

Puntanen, Simo, and George P. H. Styan. "The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator." American Statistician 43, no. 3 (August 1989): 153. http://dx.doi.org/10.2307/2685062.

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14

Puntanen, Simo, and George P. H. Styan. "The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator." American Statistician 43, no. 3 (August 1989): 153–61. http://dx.doi.org/10.1080/00031305.1989.10475644.

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15

Thomas, P. Yageen. "Estimation of the Parameters of the Uniform Distribution Over [kθ, (k+ 1)θ]." Calcutta Statistical Association Bulletin 46, no. 3-4 (September 1996): 263–68. http://dx.doi.org/10.1177/0008068319960310.

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From the available literature on estimation of the parameters of the uniform distribution over [ kθ, kθ + θ], we find the necessity to construct improved estimators of the parameter θ when k is known. In this paper a new estimator of θ is proposed when k is known and its performance is compared with best linear unbiased estimator of θ based on two extreme observations. A MS Subject Classification: Primary: 62H12; Secondary: 62G30, 62B05.

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16

Kempthorne, Oscar. "[The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator]: Comment." American Statistician 43, no. 3 (August 1989): 161. http://dx.doi.org/10.2307/2685063.

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17

Searle, Shayle R. "[The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator]: Comment." American Statistician 43, no. 3 (August 1989): 162. http://dx.doi.org/10.2307/2685064.

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18

Puntanen, Simo, and George P. H. Styan. "[The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator]: Reply." American Statistician 43, no. 3 (August 1989): 164. http://dx.doi.org/10.2307/2685065.

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19

Farebrother, R. W. "A Best Linear Unbiased Estimator of Rβ with a Scalar Variance Matrix." Econometric Theory 6, no. 4 (December 1990): 490. http://dx.doi.org/10.1017/s0266466600005569.

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20

Neudecker, H., and A. Satorra. "A Best Linear Unbiased Estimator of Rβ with α Scalar Variance Matrix." Econometric Theory 8, no. 01 (March 1992): 159–60. http://dx.doi.org/10.1017/s0266466600010938.

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21

Meyer, Luc, Dalil Ichalal, and Vincent Vigneron. "A new unbiased minimum variance observer for stochastic LTV systems with unknown inputs." IMA Journal of Mathematical Control and Information 37, no. 2 (March 20, 2019): 475–96. http://dx.doi.org/10.1093/imamci/dnz009.

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Abstract This paper is devoted to the state and input estimation of a linear time varying system in the presence of an unknown input (UI) in both state and measurement equations, and affected by Gaussian noises. The classical rank condition used in this kind of approach is relaxed in order to be able to be used in a wider range of systems. A state observer, that is an unbiased estimator with minimum error variance, is proposed. Then a UI observer is constructed, in order to be a best linear unbiased estimator, it follows a unique construction whether the direct feedthrough matrix is null or not. In a sense the proposed approach, generalizes and unifies the existing ones. Besides, a stability result is given for linear time invariant systems, which is a novelty for unbiased minimum variance observers relaxing the classical rank condition.

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22

Mäkinen, J. "Bounds for the difference between a linear unbiased estimate and the best linear unbiased estimate." Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy 25, no. 9-11 (January 2000): 693–98. http://dx.doi.org/10.1016/s1464-1895(00)00107-1.

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23

Balakrishnan, N., and C. R. Rao. "Some efficiency properties of best linear unbiased estimators." Journal of Statistical Planning and Inference 113, no. 2 (May 2003): 551–55. http://dx.doi.org/10.1016/s0378-3758(02)00107-6.

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24

Barnett, Vic, and Marion Bown. "Best linear unbiased quantile estimators for environmental standards." Environmetrics 13, no. 3 (2002): 295–310. http://dx.doi.org/10.1002/env.519.

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25

Schaden, Daniel, and Elisabeth Ullmann. "Asymptotic Analysis of Multilevel Best Linear Unbiased Estimators." SIAM/ASA Journal on Uncertainty Quantification 9, no. 3 (January 2021): 953–78. http://dx.doi.org/10.1137/20m1321607.

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26

Klápště, J., M. Lstibůrek, and J. Kobliha. "Initial evaluation of half-sib progenies of Norway spruce using the best linear unbiased prediction." Journal of Forest Science 53, No. 2 (January 7, 2008): 41–46. http://dx.doi.org/10.17221/2136-jfs.

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The present paper deals with data obtained from fifteen years old Norway spruce (<i>Picea abies</i> [L.] Karst.) progeny test established at three sites in the Sázava River region. Parameter under the evaluation was a tree height in 15 years following the establishment of the trial. Genetic parameters were estimated using the REML (Restricted Maximum Likelihood) procedure followed by the BLUP (Best Linear Unbiased Prediction). Genetic parameters estimates were used to predict genetic gain in three alternative selection strategies. The value of gain depends on target value of gene diversity. 10−15% gain is due to selecting breeding population composed of 50 individuals. Based on these quantitative findings, current and future research orientation is discussed.

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27

Comuniello, Antonella, Antonio Moschitta, and Alessio De Angelis. "Ultrasound TDoA Positioning Using the Best Linear Unbiased Estimator and Efficient Anchor Placement." IEEE Transactions on Instrumentation and Measurement 69, no. 5 (May 2020): 2477–86. http://dx.doi.org/10.1109/tim.2019.2958011.

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28

SUGIYAMA, M., M. KAWANABE, G. BLANCHARD, and K. R. MULLER. "Approximating the Best Linear Unbiased Estimator of Non-Gaussian Signals with Gaussian Noise." IEICE Transactions on Information and Systems E91-D, no. 5 (May 1, 2008): 1577–80. http://dx.doi.org/10.1093/ietisy/e91-d.5.1577.

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29

Bouriquet, Bertrand, and Jean-Philippe Argaud. "Best Linear Unbiased Estimation of the nuclear masses." Annals of Nuclear Energy 38, no. 9 (September 2011): 1863–66. http://dx.doi.org/10.1016/j.anucene.2011.05.014.

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30

Härtler, Gisela. "Best linear unbiased estimation for the Weibull process." Microelectronics Reliability 34, no. 7 (July 1994): 1253–60. http://dx.doi.org/10.1016/0026-2714(94)90511-8.

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31

Song, Guang-Jing. "On the best linear unbiased estimator and the linear sufficiency of a general growth curve model." Journal of Statistical Planning and Inference 141, no. 8 (August 2011): 2700–2710. http://dx.doi.org/10.1016/j.jspi.2011.02.021.

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32

Mu, Weiyan, Qiuyue Wei, Dongli Cui, and Shifeng Xiong. "Best Linear Unbiased Prediction for Multifidelity Computer Experiments." Mathematical Problems in Engineering 2018 (June 7, 2018): 1–7. http://dx.doi.org/10.1155/2018/8525736.

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Recently it becomes a growing trend to study complex systems which contain multiple computer codes with different levels of accuracy, and a number of hierarchical Gaussian process models are proposed to handle such multiple-fidelity codes. This paper derives the best linear unbiased prediction for three popular classes of multiple-level Gaussian process models. The predictors all have explicit expressions at each untried point. Empirical best linear unbiased predictors are also provided by plug-in methods with generalized maximum likelihood estimators of unknown parameters.

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33

Kott, Phillip S. "When a Mean-of-Ratios is the Best Linear Unbiased Estimator Under a Model." American Statistician 40, no. 3 (August 1986): 202. http://dx.doi.org/10.2307/2684536.

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34

Kott, Phillip S. "When a Mean-of-Ratios is the Best Linear Unbiased Estimator under a Model." American Statistician 40, no. 3 (August 1986): 202–4. http://dx.doi.org/10.1080/00031305.1986.10475393.

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35

Zmyślony, Roman, João T. Mexia, Francisco Carvalho, and Inês J. Sequeira. "Mean driven balance and uniformly best linear unbiased estimators." Statistical Papers 57, no. 1 (October 30, 2014): 43–53. http://dx.doi.org/10.1007/s00362-014-0638-y.

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36

WENLI, YANG, CUI HENGJIAN, and SUN GUOWEN. "On Best Linear Unbiased Estimation in the Restricted General Linear Model." Statistics 18, no. 1 (January 1987): 17–20. http://dx.doi.org/10.1080/02331888708801985.

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37

Sara McPeek, Mary, Xiaodong Wu, and Carole Ober. "Best Linear Unbiased Allele-Frequency Estimation in Complex Pedigrees." Biometrics 60, no. 2 (June 2004): 359–67. http://dx.doi.org/10.1111/j.0006-341x.2004.00180.x.

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38

Villanueva, Beatriz, and Javier Moro. "Variance and efficiency of the combined estimator in incomplete block designs of use in forest genetics: a numerical study." Canadian Journal of Forest Research 31, no. 1 (January 1, 2001): 71–77. http://dx.doi.org/10.1139/x00-138.

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The efficiency of combined interblock-intrablock and intrablock analysis for the estimation of treatment contrasts in alpha designs is compared using Monte-Carlo simulation. The combined estimator considers treatments and replications as fixed effects and blocks as random effects, whereas the intrablock estimator considers treatments, replications, and blocks as fixed effects. The variances of the estimators are used as the criterion for comparison. The combined estimator yields more accurate estimates than the intrablock estimator when the ratio of the block to the error variance is small, especially for designs with the fewest degrees of freedom. The accuracy of both estimators is similar when the ratio of variances is large. The variance of the combined estimator is very close to that of the best linear unbiased estimator except for designs with small number of replicates and families or provenances. Approximations commonly used for the variance of the combined estimator when variances of the random effects are unknown are studied. The downward or negative bias in the estimates of the variance given by the standard approximation used in statistical packages is largest under the conditions in which the combined estimator is more efficient than the intrablock estimator. Estimates of the relative efficiency of combined estimators have an upward bias that can exceed 10% of the true value in small- and middle-sized designs with two or three replicates. In designs with four or more replicates, often used in forest genetics, the bias is negligible.

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39

Zarnoch, S. J., and W. A. Bechtold. "Estimating mapped-plot forest attributes with ratios of means." Canadian Journal of Forest Research 30, no. 5 (May 1, 2000): 688–97. http://dx.doi.org/10.1139/x99-247.

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The mapped-plot design utilized by the U.S. Department of Agriculture (USDA) Forest Inventory and Analysis and the National Forest Health Monitoring Programs is described. Data from 2458 forested mapped plots systematically spread across 25 states reveal that 35% straddle multiple conditions. The ratio-of-means estimator is developed as a method to obtain estimates of forest attributes from mapped plots, along with measures of variability useful for constructing confidence intervals. Basic inventory statistics from North and South Carolina were examined to see if these data satisfied the conditions necessary to qualify the ratio of means as the best linear unbiased estimator. It is shown that the ratio-of-means estimator is equivalent to the Horwitz-Thompson, the mean-of-ratios, and the weighted-mean-of-ratios estimators under certain situations.

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40

Luskin, Robert C. "Wouldn't It Be Nice …? The Automatic Unbiasedness of OLS (and GLS)." Political Analysis 16, no. 3 (2008): 345–49. http://dx.doi.org/10.1093/pan/mpn003.

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In a recent issue of this journal, Larocca (2005) makes two notable claims about the best linear unbiasedness of ordinary least squares (OLS) estimation of the linear regression model. The first, drawn from McElroy (1967), is that OLS remains best linear unbiased in the face of a particular kind of autocorrelation (constant for all pairs of observations). The second, much larger and more heterodox, is that the disturbance need not be assumed uncorrelated with the regressors for OLS to be best linear unbiased. The assumption is unnecessary, Larocca says, because “orthogonality [of disturbance and regressors] is a property of all OLS estimates” (p. 192). Of course OLS's being best linear unbiased still requires that the disturbance be homoskedastic and (McElroy's loophole aside) nonautocorrelated, but Larocca also adds that the same automatic orthogonality obtains for generalized least squares (GLS), which is also therefore best linear unbiased, when the disturbance is heteroskedastic or autocorrelated.

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41

Adatia, A. "Best linear unbiased estimator of the Rayleigh scale parameter based on fairly large censored samples." IEEE Transactions on Reliability 44, no. 2 (June 1995): 302–9. http://dx.doi.org/10.1109/24.387386.

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42

Rakhsyanda, Naima, Kusman Sadik, and Indahwati Indahwati. "Simulation Study of Robust Geographically Weighted Empirical Best Linear Unbiased Predictor on Small Area Estimation." Indonesian Journal of Statistics and Its Applications 5, no. 1 (March 31, 2021): 50–60. http://dx.doi.org/10.29244/ijsa.v5i1p50-60.

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Small area estimation can be used to predict the population parameter with small sample sizes. For some cases, the population units that are close spatially may be more related than units that are further apart. The use of spatial information like geographic coordinates are studied in this research. Outlier contaminations can affect small area estimations. This study was conducted using simulation methods on generated data with six scenarios. The scenarios are the combination of spatial effects (spatial stationary and spatial non-stationary) with outlier contamination (no outlier, symmetric outliers, and non-symmetric outliers). The purpose of this study was to compare the geographically weighted empirical best linear unbiased predictor (GWEBLUP) and robust GWEBLUP (RGWEBLUP) with direct estimator, EBLUP, and REBLUP using simulation data. The performance of the predictors is evaluated using relative root mean squared error (RRMSE). The simulation results showed that geographically weighted predictors have the smallest RRMSE values for scenarios with spatial non-stationary, therefore offer a better prediction. For scenarios with outliers, robust predictors with smaller RRMSE values offer more efficiency than non-robust predictors.

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43

Wyszkowska, P., and R. Duchnowski. "Systematic bias of selected estimates applied in vertical displacement analysis." Journal of Geodetic Science 10, no. 1 (June 2, 2020): 41–47. http://dx.doi.org/10.1515/jogs-2020-0103.

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AbstractIn surveying problems we almost always use unbiased estimators; however, even unbiased estimator might yield biased assessments, which is due to data. In statistics one distinguishes several types of such biases, for example, sampling, systemic or response biases. Considering surveying observation sets, bias from data might result from systematic or gross errors of measurements. If nonrandom errors in an observation set are known, then bias can easily be determined for linear estimates (e.g., least squares estimates). In the case of non-linear estimators, it is not so simple. In this paper we are focused on a vertical displacement analysis and we consider traditional least squares estimate, two Msplitestimates and two basic robust estimates, namely M-estimate, R-estimate. The main aim of the paper is to assess estimate biases empirically by applying Monte Carlo method. The smallest biases are obtained for M- and R-estimates, especially for a high magnitude of a gross error. On the other hand, there are several cases when Msplitestimates are the best. Such results are acquired when the magnitude of a gross error is moderate or small. The outcomes confirm that bias of Msplitestimates might vary for different point displacements.

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44

Yoon, Jin Hee, and Przemyslaw Grzegorzewski. "On Optimal and Asymptotic Properties of a Fuzzy L2 Estimator." Mathematics 8, no. 11 (November 4, 2020): 1956. http://dx.doi.org/10.3390/math8111956.

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A fuzzy least squares estimator in the multiple with fuzzy-input–fuzzy-output linear regression model is considered. The paper provides a formula for the L2 estimator of the fuzzy regression model. This paper proposes several operations for fuzzy numbers and fuzzy matrices with fuzzy components and discussed some algebraic properties that are needed to use for proving theorems. Using the proposed operations, the formula for the variance, provided and this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. The confidence regions of the coefficient parameters and the asymptotic relative efficiency (ARE) are also discussed. In addition, several examples are provided including a Monte Carlo simulation study showing the validity of the proposed theorems.

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45

Singh, G. N., S. Prasad, and D. Majhi. "Best linear unbiased estimators of population variance in successive sampling." Model Assisted Statistics and Applications 7, no. 3 (June 25, 2012): 169–78. http://dx.doi.org/10.3233/mas-2012-0224.

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46

Dorst, Leo, and Arnold W. M. Smeulders. "Best Linear Unbiased Estimators for Properties of Digitized Straight Lines." IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-8, no. 2 (March 1986): 276–82. http://dx.doi.org/10.1109/tpami.1986.4767781.

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47

Haslett, Stephen. "Best linear unbiased estimation for varying probability with and without replacement sampling." Special Matrices 7, no. 1 (January 1, 2019): 78–91. http://dx.doi.org/10.1515/spma-2019-0007.

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Abstract When sample survey data with complex design (stratification, clustering, unequal selection or inclusion probabilities, and weighting) are used for linear models, estimation of model parameters and their covariance matrices becomes complicated. Standard fitting techniques for sample surveys either model conditional on survey design variables, or use only design weights based on inclusion probabilities essentially assuming zero error covariance between all pairs of population elements. Design properties that link two units are not used. However, if population error structure is correlated, an unbiased estimate of the linear model error covariance matrix for the sample is needed for efficient parameter estimation. By making simultaneous use of sampling structure and design-unbiased estimates of the population error covariance matrix, the paper develops best linear unbiased estimation (BLUE) type extensions to standard design-based and joint design and model based estimation methods for linear models. The analysis covers both with and without replacement sample designs. It recognises that estimation for with replacement designs requires generalized inverses when any unit is selected more than once. This and the use of Hadamard products to link sampling and population error covariance matrix properties are central topics of the paper. Model-based linear model parameter estimation is also discussed.

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48

Farsipour, N. Sanjari, and A. Asgharzadeh. "Estimating the Common Mean of k Normal Populations with Known Variance." International Journal of Statistics and Probability 6, no. 4 (June 26, 2017): 70. http://dx.doi.org/10.5539/ijsp.v6n470.

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Consider the problem of estimating the common mean of knormal populations with known variances. We study the admisibility of the Best linear Risk Unbiased Equivariant (BLRUE)estimator of the common mean of k normalpopulations underthe squared error and LINEX loss function when the variancesare known.

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49

Farsipour, N. Sanjari, and A. Asgharzadeh. "Estimating the Common Mean of k Normal Populations with Known Variance." International Journal of Statistics and Probability 6, no. 4 (June 26, 2016): 70. http://dx.doi.org/10.5539/ijsp.v6n4p70.

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Consider the problem of estimating the common mean of knormal populations with known variances. We study the admisibility of the Best linear Risk Unbiased Equivariant (BLRUE)estimator of the common mean of k normalpopulations underthe squared error and LINEX loss function when the variancesare known.

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50

Kleinknecht, K., J. Möhring, K. P. Singh, P. H. Zaidi, G. N. Atlin, and H. P. Piepho. "Comparison of the Performance of Best Linear Unbiased Estimation and Best Linear Unbiased Prediction of Genotype Effects from Zoned Indian Maize Data." Crop Science 53, no. 4 (July 2013): 1384–91. http://dx.doi.org/10.2135/cropsci2013.02.0073.

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