Admissibility of Invariant Tests for Means with Covariates

@article{Tsai2019AdmissibilityOI,
  title={Admissibility of Invariant Tests for Means with Covariates},
  author={Ming Tien Tsai},
  journal={Mathematical Methods of Statistics},
  year={2019}
}
  • M. Tsai
  • Published 3 April 2017
  • Mathematics
  • Mathematical Methods of Statistics
For a multinormal distribution with a $p$-dimensional mean vector ${\mbtheta}$ and an arbitrary unknown dispersion matrix ${\mbSigma}$, Rao ([9], [10]) proposed two tests for the problem of testing $ H_{0}:{\mbtheta}_{1} = {\bf 0}, {\mbtheta}_{2} = {\bf 0}, {\mbSigma}~ \hbox{unspecified},~\hbox{versus}~H_{1}:{\mbtheta}_{1} \ne {\bf 0}, {\mbtheta}_{2} ={\bf 0}, {\mbSigma}~\hbox{unspecified}$, where ${\mbtheta}^{'}=({\mbtheta}^{'}_{1},{\mbtheta}^{'}_{2})$. These tests are referred to as Rao's $W… 
A Complete Bibliography of Publications in Mathematical Methods of Statistics
α [589, 628, 228]. AR(1) [108]. ARCH(p) [348]. β [226, 409]. L [230]. D [281, 369, 294, 320, 148]. E [254]. f [581]. G [331]. K [456, 10]. Kn [397]. L [66, 59, 582]. l [162]. L1 [344, 439, 466]. L2
A Remark for the Admissibility of Rao’s U-test

References

SHOWING 1-10 OF 21 REFERENCES
ON AN OPTIMUM PROPERTY OF TWO IMPORTANT STATISTICAL TESTS
P. L. Hsu (1940) has shown that for any linear hypothesis the E2-test is the uniformly most powerful of all the tests whose power function depends on a certain function, A, of the population
An Introduction to Multivariate Statistical Analysis
Preface to the Third Edition.Preface to the Second Edition.Preface to the First Edition.1. Introduction.2. The Multivariate Normal Distribution.3. Estimation of the Mean Vector and the Covariance
Tests with discriminant functions in multivariate analysis
In a paper (Rao : 1946), the author has considered a general method of arriving at suitable studentised statistics which are to be used in tests of linear hypotheses when the observed set of
Testing Statistical Hypotheses
The General Decision Problem.- The Probability Background.- Uniformly Most Powerful Tests.- Unbiasedness: Theory and First Applications.- Unbiasedness: Applications to Normal Distributions.-
Admissibility: Survey of a Concept in Progress
Summary This paper surveys the study of admissibility in statistical decision theory. Reviewed are: Stein's necessary and sufficient admissibility condition and its extensions; Brown's heuristic
Inequalities: Theory of Majorization and Its Applications
Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of
Generalized Inverse of Matrices and its Applications
TLDR
The Generalized Inverse of Matrices and its Applications is studied in detail in the context of discrete-time optimization and its applications.
Testing Statistical Hypotheses, 2nd edition
  • New York: Wiley,
  • 1986
An Introduction to Multivariate Statistical Analysis, 2nd Edition.
Invariant Tests for Means with Covariates
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