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# Deficiencies Between Linear Normal Experiments

Anders Rygh Swensen
The Annals of Statistics
Vol. 8, No. 5 (Sep., 1980), pp. 1142-1155
Stable URL: http://www.jstor.org/stable/2240444
Page Count: 14
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## Abstract

Let X1, ⋯, Xn be independent and normally distributed variables, such that $0 < \operatorname{Var} X_i = \sigma^2, i = 1, \cdots, n$ and E(X1, ⋯, Xn)' = A'β where A is a k × n matrix with known coefficients and β = (β1, ⋯, βk)' is an unknown vector. σ may be known or unknown. Denote the experiment obtained by observing X1, ⋯, Xn by EA. Let A and B be matrices of dimension nA × k and nB × k. The deficiency δ(EA, EB) is computed when σ is known and for some cases, including the case BB' - AA' positive semidefinite and AA' nonsingular, also when σ is unknown. The technique used consists of reducing to testing a composite hypotheses and finding a least favorable distribution.

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