Further research on simple projection prediction under a general linear model

doi:10.3868/s140-DDD-024-0016-x

Front. Math. China

2024, Vol. 19

Issue (5) : 255-275 https://doi.org/10.3868/s140-DDD-024-0016-x

Further research on simple projection prediction under a general linear model

Bo JIANG¹, Luping WANG¹, Yongge TIAN²(

)

¹. College of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
². College of Business and Economics, Shanghai Business School, Shanghai 201400, China

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Abstract

Linear model is a kind of important model in statistics. The estimation and prediction of unknown parameters in the model is a basic problem in statistical inference. According to different evaluation criteria, different forms of predictors are obtained. The simple projection prediction (SPP) boasts simple form while the best linear unbiased prediction (BLUP) enjoys very excellent properties. Naturally, the relationship between the two predictors are considered. We give the necessary and sufficient conditions for the equality of SPP and BLUP. Finally, we study the robustness of SPP and BLUP with respect to covariance matrix and illustrate the application of equivalence conditions by use of error uniform correlation models.

Keywords Linear model SPP BLUP equivalence robustness

Corresponding Author(s): Yongge TIAN

Online First Date: 15 October 2024 Issue Date: 31 October 2024

Cite this article:

Bo JIANG,Luping WANG,Yongge TIAN. Further research on simple projection prediction under a general linear model[J]. Front. Math. China, 2024, 19(5): 255-275.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-024-0016-x
https://academic.hep.com.cn/fmc/EN/Y2024/V19/I5/255

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