On relations between weighted least-squares estimators of parametric functions under a general partitioned linear model and its small models

Changli Lu (), Yuqin Sun () and Yongge Tian ()

Metrika: International Journal for Theoretical and Applied Statistics, 2013, vol. 76, issue 5, 707-722

Abstract: We study relations between the weighted least-squares estimators (WLSEs) of given parametric functions $$\mathbf{K}_1\varvec{\beta }_1 + \mathbf{K}_2\varvec{\beta }_2$$ under a general partitioned linear model $${\fancyscript{M}}=\{ \mathbf{y}, \, \mathbf{X}_1\varvec{\beta }_1 + \mathbf{X}_2\varvec{\beta }_2, \, \sigma ^2\varvec{\Sigma }\}$$ and the WLSEs of $$\mathbf{K}_1\varvec{\beta }_1$$ and $$\mathbf{K}_2\varvec{\beta }_2$$ under the two small models $$\{ \mathbf{y}, \, \mathbf{X}_1\varvec{\beta }_1, \, \sigma ^2\varvec{\Sigma }\}$$ and $$\{ \mathbf{y}, \, \mathbf{X}_2\varvec{\beta }_2, \,\sigma ^2\varvec{\Sigma }\}$$ . Some consequences on additive decomposition of the best unbiased linear estimator (BLUE) of $$\mathbf{K}_1\varvec{\beta }_1 + \mathbf{K}_2\varvec{\beta }_2$$ under $${\fancyscript{M}}$$ are also given. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Partitioned linear model; Small models; Parametric functions; WLSE; BLUE; Decomposition of estimator; Moore–Penrose inverse of matrix (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00184-012-0412-x

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