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September, 1980 Deficiencies Between Linear Normal Experiments
Anders Rygh Swensen
Ann. Statist. 8(5): 1142-1155 (September, 1980). DOI: 10.1214/aos/1176345151

Abstract

Let $X_1, \cdots, X_n$ be independent and normally distributed variables, such that $0 < \operatorname{Var} X_i = \sigma^2, i = 1, \cdots, n$ and $E(X_1, \cdots, X_n)' = A'\beta$ where $A$ is a $k \times n$ matrix with known coefficients and $\beta = (\beta_1, \cdots, \beta_k)'$ is an unknown vector. $\sigma$ may be known or unknown. Denote the experiment obtained by observing $X_1, \cdots, X_n$ by $\mathscr{E}_A.$ Let $A$ and $B$ be matrices of dimension $n_A \times k$ and $n_B \times k.$ The deficiency $\delta(\mathscr{E}_A, \mathscr{E}_B)$ is computed when $\sigma$ is known and for some cases, including the case $BB' - AA'$ positive semidefinite and $AA'$ nonsingular, also when $\sigma$ is unknown. The technique used consists of reducing to testing a composite hypotheses and finding a least favorable distribution.

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Anders Rygh Swensen. "Deficiencies Between Linear Normal Experiments." Ann. Statist. 8 (5) 1142 - 1155, September, 1980. https://doi.org/10.1214/aos/1176345151

Information

Published: September, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0445.62007
MathSciNet: MR585712
Digital Object Identifier: 10.1214/aos/1176345151

Subjects:
Primary: 62B15
Secondary: 62K99

Keywords: additional observations , Deficiencies , invariant kernels , normal models

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 5 • September, 1980
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