Linear prediction sufficiency in the misspecified linear model. Issue 21 (21st September 2020)

• Record Type: Journal Article
• Authors: Markiewicz, Augustyn; Puntanen, Simo
• Is Part Of: Communications in statistics. Volume 50:Issue 21(2021)
• Page Start: 4977
• Page End: 4996
• Publication Date: 2020-09-21
• Subjects: BLUE -- best linear unbiased estimator -- BLUP -- best linear unbiased predictor -- linear model -- linear model with new observations -- linear sufficiency; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1584311
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: We consider the general linear model y = X β + ε supplemented with the new (future) unobservable random vector y *, coming from y * = X * β + ε *, where the expectation of y * is X * β and the covariance matrix of y * is known as well as the cross-covariance matrix between y * and y . We denote the supplemented model as M * . The misspecified supplemented model is denoted as M ¯ *, and the misspecification concerns the covariance part of the setup. Suppose that Fy is linearly sufficient for estimable parametric function X * β under M * . We give necessary and sufficient conditions that Fy continues to be linearly sufficient for X * β under the model M ¯ * . The corresponding properties regarding the linear prediction sufficiency with respect to ε * and y * are also studied.