On MSE of EBLUP

Abstract We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Ża̧dło, Tomasz [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	2007

Schlagwörter:	Model approach in survey sampling General linear model General mixed linear model BLUP and EBLUP

Anmerkung:	© Springer-Verlag 2007

Übergeordnetes Werk:	Enthalten in: Statistical papers - Springer-Verlag, 1988, 50(2007), 1 vom: 06. Juni, Seite 101-118
Übergeordnetes Werk:	volume:50 ; year:2007 ; number:1 ; day:06 ; month:06 ; pages:101-118

Links:	Volltext

DOI / URN:	10.1007/s00362-007-0066-3

Katalog-ID:	OLC2025020937

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allfields	10.1007/s00362-007-0066-3 doi (DE-627)OLC2025020937 (DE-He213)s00362-007-0066-3-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Ża̧dło, Tomasz verfasserin aut On MSE of EBLUP 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study. Model approach in survey sampling General linear model General mixed linear model BLUP and EBLUP Enthalten in Statistical papers Springer-Verlag, 1988 50(2007), 1 vom: 06. Juni, Seite 101-118 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:50 year:2007 number:1 day:06 month:06 pages:101-118 https://doi.org/10.1007/s00362-007-0066-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_4027 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4700 AR 50 2007 1 06 06 101-118
spelling	10.1007/s00362-007-0066-3 doi (DE-627)OLC2025020937 (DE-He213)s00362-007-0066-3-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Ża̧dło, Tomasz verfasserin aut On MSE of EBLUP 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study. Model approach in survey sampling General linear model General mixed linear model BLUP and EBLUP Enthalten in Statistical papers Springer-Verlag, 1988 50(2007), 1 vom: 06. Juni, Seite 101-118 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:50 year:2007 number:1 day:06 month:06 pages:101-118 https://doi.org/10.1007/s00362-007-0066-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_4027 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4700 AR 50 2007 1 06 06 101-118
allfields_unstemmed	10.1007/s00362-007-0066-3 doi (DE-627)OLC2025020937 (DE-He213)s00362-007-0066-3-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Ża̧dło, Tomasz verfasserin aut On MSE of EBLUP 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study. Model approach in survey sampling General linear model General mixed linear model BLUP and EBLUP Enthalten in Statistical papers Springer-Verlag, 1988 50(2007), 1 vom: 06. Juni, Seite 101-118 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:50 year:2007 number:1 day:06 month:06 pages:101-118 https://doi.org/10.1007/s00362-007-0066-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_4027 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4700 AR 50 2007 1 06 06 101-118
allfieldsGer	10.1007/s00362-007-0066-3 doi (DE-627)OLC2025020937 (DE-He213)s00362-007-0066-3-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Ża̧dło, Tomasz verfasserin aut On MSE of EBLUP 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study. Model approach in survey sampling General linear model General mixed linear model BLUP and EBLUP Enthalten in Statistical papers Springer-Verlag, 1988 50(2007), 1 vom: 06. Juni, Seite 101-118 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:50 year:2007 number:1 day:06 month:06 pages:101-118 https://doi.org/10.1007/s00362-007-0066-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_4027 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4700 AR 50 2007 1 06 06 101-118
allfieldsSound	10.1007/s00362-007-0066-3 doi (DE-627)OLC2025020937 (DE-He213)s00362-007-0066-3-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Ża̧dło, Tomasz verfasserin aut On MSE of EBLUP 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study. Model approach in survey sampling General linear model General mixed linear model BLUP and EBLUP Enthalten in Statistical papers Springer-Verlag, 1988 50(2007), 1 vom: 06. Juni, Seite 101-118 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:50 year:2007 number:1 day:06 month:06 pages:101-118 https://doi.org/10.1007/s00362-007-0066-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_4027 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4700 AR 50 2007 1 06 06 101-118
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source	Enthalten in Statistical papers 50(2007), 1 vom: 06. Juni, Seite 101-118 volume:50 year:2007 number:1 day:06 month:06 pages:101-118
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author	Ża̧dło, Tomasz
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title	On MSE of EBLUP
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title_full	On MSE of EBLUP
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title_sort	on mse of eblup
title_auth	On MSE of EBLUP
abstract	Abstract We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study. © Springer-Verlag 2007
abstractGer	Abstract We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study. © Springer-Verlag 2007
abstract_unstemmed	Abstract We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study. © Springer-Verlag 2007
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Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. 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