|
|||||
|
|
Locally minimax tests for multiple correlations |
|
| Authors: | N. Giri |
| Abstract: | Let X be a normally distributed p-dimensional column vector with mean μ and positive definite covariance matrix σ. and let X α, α = 1,…, N, be a random sample of size N from this distribution. Partition X as ( X 1, X (2)', X '(3))', where X1 is one-dimension, X(2) is p2- dimensional, and so 1 + p1 + p2 = p. Let ρ1 and ρ be the multiple correlation coefficients of X1 with X(2) and with ( X '(2), X '(3))', respectively. Write ρ2/2 = ρ2 - ρ2/1. We shall cosider the following two problems |
| Keywords: | Likelihood-ratio test locally minimax test Hotelling's T2 test R2-test admissible test Hunt-Stein theorem invariant test minimax test |