On two correlated linear models with common and different parameters
-
Bo Jiang
Abstract
A parametric regression model may comprise several correlated individual regression equations, and these equations may have common and different unknown parameters. In such a situation, the common unknown parameter vectors in these equations can be estimated individually or simultaneously according to various available statistical inference methods. The purpose of this paper is to provide an integral account of two classic objects in regression theory: the best linear unbiased predictors (BLUPs) and the best linear unbiased estimators (BLUEs) on common and different unknown parameters in two correlated linear models with common and different parameters. We first introduce some reduced models associated with the two correlated linear models. We then define and characterize predictability and estimability of all unknown parameter vectors in the two correlated models and their reduced models, and derive analytical formulas for calculating the BLUPs and BLUEs of all unknown parameter vectors in these models by means of a constrained quadratic matrix optimization method. We also discuss a variety of theoretical properties of the predictors and estimators.
We wish to thank two anonymous referees for their helpful comments and suggestions on an earlier version of this article. This work is supported by the Shandong Provincial Natural Science Foundation #ZR2019MA065.
(Communicated by Gejza Wimmer )
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Articles in the same Issue
- Regular Papers
- Generalized hyperharmonic number sums with reciprocal binomial coefficients
- Gini index on generalized r-partitions
- Multiplicative functions of special type on Piatetski-Shapiro sequences
- Strengthenings of Young-type inequalities and the arithmetic geometric mean inequality
- Generalizations of the steffensen integral inequality for pseudo-integrals
- Subordination-implication problems concerning the nephroid starlikeness of analytic functions
- Boundedness and almost periodicity of solutions of linear differential systems
- On variational approaches for fractional differential equations
- Approximity of asymmetric metric spaces
- Approximation theorems for the new construction of Balázs operators and its applications
- On η-biharmonic hypersurfaces in pseudo-Riemannian space forms
- Chen’s first inequality for hemi-slant warped products in nearly trans-Sasakian manifolds
- Induced mappings on symmetric products of Hausdorff spaces
- The Teissier-G family of distributions: Properties and applications
- A new extension of the beta generator of distributions
- A new family of compound exponentiated logarithmic distributions with applications to lifetime data
- On two correlated linear models with common and different parameters
- On some applications of Duhamel operators
