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Parametric regression models with certain parameter restrictions occur widely in statistical data analysis and inference. In some cases, we may wish to impose linear constraints on some subsets of fixed parameters in a given parametric regression model. This paper is concerned with some fundamental inference problems on a general linear model y = X β + ε in which the unknown parameter vector β is subject to a linear matrix equation restriction A β = b . We shall introduce the technical concepts and definitions of consistency, predictability, estimability, and formulas of the best linear unbiased predictors/best linear unbiased estimators (BLUPs/BLUEs) under a constrained general linear model (CGLM). We then show how to establish BLUPs/BLUEs of all unknown parameters in the CGLM, and present various properties of the BLUPs/BLUEs using the methodology of matrix ranks and inertias. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new method which corrects residual variances for the butterfly distributed residuals (BDR). Distribution theory, confidence intervals, and tests of hypotheses are valid and meaningful only if the standard regression assumptions are satisfied. Heteroskedasticity is one of the violations of these assumptions and BDR is another type of heteroskedasticity. This study reveals an alternative approach to correct the BDR type of heteroskedasticity by the weighting re-estimated absolute residuals (WRAR). After giving brief information about heteroskedasticity and BDR type of heteroskedasticity, WRAR is introduced. WRAR and the usual variance stabilizing techniques are compared on multiple and simple regression models. [ABSTRACT FROM AUTHOR]

Building on the work of Lustbader and Moolgavkar (1985), this paper studies influence diagnostics for score tests. The diagnostic proposed by Lustbader and Moolgavkar is reassessed, and alternative diagnostics are proposed. The new diagnostics are based on one-step approximations to the change in the parameter estimates, resulting from deleting one observation. The use of the different diagnostics is illustrated with simulations and with an example. [ABSTRACT FROM AUTHOR]