Stability of invariant linearly sufficient statistics in the general Gauss-Markov model

Andrzej Kornacki

Applications of Mathematics (1997)

  • Volume: 42, Issue: 1, page 71-77
  • ISSN: 0862-7940

Abstract

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Necessary and sufficient conditions are derived for the inclusions J 0 ⊂ J and J 0 * ⊂ J * to be fulfilled where J 0 , J 0 * and J , J * are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models G M 0 = ( y , X 0 β 0 , σ 0 2 V 0 ) and G M = ( y , X β , σ 2 V ) , respectively.

How to cite

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Kornacki, Andrzej. "Stability of invariant linearly sufficient statistics in the general Gauss-Markov model." Applications of Mathematics 42.1 (1997): 71-77. <http://eudml.org/doc/32968>.

@article{Kornacki1997,
abstract = {Necessary and sufficient conditions are derived for the inclusions $J_0\subset J$ and $J_0^\{*\}\subset J^\{*\}$ to be fulfilled where $J_0$, $J_0^\{*\}$ and $J$, $J^\{*\}$ are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models $GM_0=(y,X_0\beta _0,\sigma _0^2V_0)$ and $GM=(y,X\beta ,\sigma ^2V)$, respectively.},
author = {Kornacki, Andrzej},
journal = {Applications of Mathematics},
keywords = {Gauss-Markov model; linearly sufficient statistics; invariant linearly sufficient statistics; Gauss-Markov model; invariant linearly sufficient statistics},
language = {eng},
number = {1},
pages = {71-77},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability of invariant linearly sufficient statistics in the general Gauss-Markov model},
url = {http://eudml.org/doc/32968},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Kornacki, Andrzej
TI - Stability of invariant linearly sufficient statistics in the general Gauss-Markov model
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 1
SP - 71
EP - 77
AB - Necessary and sufficient conditions are derived for the inclusions $J_0\subset J$ and $J_0^{*}\subset J^{*}$ to be fulfilled where $J_0$, $J_0^{*}$ and $J$, $J^{*}$ are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models $GM_0=(y,X_0\beta _0,\sigma _0^2V_0)$ and $GM=(y,X\beta ,\sigma ^2V)$, respectively.
LA - eng
KW - Gauss-Markov model; linearly sufficient statistics; invariant linearly sufficient statistics; Gauss-Markov model; invariant linearly sufficient statistics
UR - http://eudml.org/doc/32968
ER -

References

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  1. Linear sufficiency and completeness in an incorrectly specified general Gauss-Markov model, Sankhyā, Ser A. 48 (1986), 169–180. (1986) MR0905457
  2. Sufficiency and completeness in the general Gauss-Markoff model, Sankhyā, Ser A. 45 (1983), 88–98. (1983) MR0749356
  3. 10.1080/03610928108828078, Comm. Statistics—A, Theory Methods 10 (1981), 849–873. (1981) Zbl0465.62060MR0625196DOI10.1080/03610928108828078
  4. 10.1016/0378-3758(83)90048-4, J. Statist Plann. Inference 8 (1983), 315–329. (1983) MR0729248DOI10.1016/0378-3758(83)90048-4
  5. Invariant linearly sufficient transformations of the general Gauss-Markoff model, Scand. J Statist. 15 (1988), 117–124. (1988) MR0968158
  6. Unified theory of linear estimation, Sankhyā A 35 (1971), 371–394. (1971) Zbl0236.62048MR0319321
  7. Generalized Inverse of Matrices and its Applications, Wiley, New York, 1971. (1971) MR0338013

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