Probabilistic-statistical models

Formula for the limit of the normalized difference between the powers of the asymptotically most powerful test and asymptotically optimal test for the case of Laplace distribution

R. A. Korolev

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: In the paper we prove a formula for the limit of thе normalized difference between the power of the asymptotically most powerful test and the power of the asymptotically optimal test for the case of Laplace distribution. The asymptotically optimal test is based on the sign statistic which has a lattice distribution, and an analog of Cramér's (C) condition is valid for the logarithm of the likelihood ratio. Thereby we can not use the main formula 3.2.1 from [1] directly. In this paper we suggest a combined method based on the convergence of the conditional moments and on the asymptotic expansions.

Keywords: asymptotic expansion, lattice statistic or distribution, power function, conditional moment, Laplace or double exponential distribution.

UDC: 519.2

Received: 20.01.2010
Revised: 22.01.2010

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