LRT conjecture for bivariate normal

Walid Abu‐Dayyeh

doi:10.1016/S0096-3003(02)00470-8

LRT conjecture for bivariate normal

2003-12-01

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DOI：10.1016/S0096-3003(02)00470-8

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In this paper, we consider testing H-0 : (theta(1), theta(2)) = (0, 0) vs H-1 : (theta(1), theta(2)) is an element of Theta - {(0, 0)}, where Theta is a closed square with center at the origin in the case of a bivariate normal distribution with mean vector (theta(1), theta(2)) and identity covariance matrix. We show by numerical calculations that the conjecture of Marden [1982], which says that if more restrictions are put on the alternative space, then the power of the LRT increases, is not true in this case. Moreover, some properties of the LRT are given. (C) 2002 Elsevier Inc. All rights reserved.

Keyword:

LRT conjecture

restricted alternative space

power function

convexity

monotonicity

LRT conjecture for bivariate normal

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