Asymptotic normality and consistency of a two-stage generalized least squares estimator in the growth curve model
| dc.creator | Hu, Jianhua | |
| dc.creator | Yan, Guohua | |
| dc.date | 2008-10-22 | |
| dc.date.accessioned | 2026-07-07T10:12:25Z | |
| dc.date.available | 2026-07-07T10:12:25Z | |
| dc.description | Let $\mathbf{Y}=\mathbf{X}\boldsΘ\mathbf{Z}'+\bolds{\mathcal {E}}$ be the growth curve model with $\bolds{\mathcal{E}}$ distributed with mean $\mathbf{0}$ and covariance $\mathbf{I}_n\otimes\boldsΣ$, where $\boldsΘ$, $\boldsΣ$ are unknown matrices of parameters and $\mathbf{X}$, $\mathbf{Z}$ are known matrices. For the estimable parametric transformation of the form $\bolds γ=\mathbf{C}\boldsΘ\mathbf{D}'$ with given $\mathbf{C}$ and $\mathbf{D}$, the two-stage generalized least-squares estimator $\hat{\bolds γ}(\mathbf{Y})$ defined in (7) converges in probability to $\boldsγ$ as the sample size $n$ tends to infinity and, further, $\sqrt{n}[\hat{\boldsγ}(\mathbf{Y})-\bolds γ]$ converges in distribution to the multivariate normal distribution $\ma thcal{N}(\mathbf{0},(\mathbf{C}\mathbf{R}^{-1}\mathbf{C}')\otimes(\mat hbf{D}(\mathbf{Z}'\boldsΣ^{-1}\mathbf{Z})^{-1}\mathbf{D}'))$ under the condition that $\lim_{n\to\infty}\mathbf{X}'\mathbf{X}/n=\mathbf{R}$ for some positive definite matrix $\mathbf{R}$. Moreover, the unbiased and invariant quadratic estimator $\hat{\boldsΣ}(\mathbf{Y})$ defined in (6) is also proved to be consistent with the second-order parameter matrix $\boldsΣ$. | |
| dc.description | Published in at http://dx.doi.org/10.3150/08-BEJ128 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) | |
| dc.identifier | https://arxiv.org/abs/0810.3995 | |
| dc.identifier | http://arxiv.org/abs/0810.3995 | |
| dc.identifier | Bernoulli 2008, Vol. 14, No. 3, 623-636 | |
| dc.identifier | doi:10.3150/08-BEJ128 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172176 | |
| dc.subject | Statistics Theory | |
| dc.title | Asymptotic normality and consistency of a two-stage generalized least squares estimator in the growth curve model | |
| dc.type | text |