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On Asymptotically Exact Testing of Nonparametric Hypotheses

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  • LEPSKII , Oleg V.

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium and Institute for System Analysis, Russian Academy of Sciences, Moscow, Russian)

Abstract

This paper deals with testing of nonparametric hypotheses when the model of observation is unknown function [ sigma (.)] plus a Gaussian White Noise with a small diffusion [ epsilon > 0 ]. It is required to distinguish the simple hypothesis H_0 : [ sigma(.) ] = 0 against the composite alternative H_[ epsilon] : [ sigma(.) ][ is an element of ][ summation_epsilon], where [summation_epsilon] is a certain class of smooth functions, separated from zero by the value [ C psi (epsilon)], that is described by some functional ( the function [ psi (epsilon)] and the constant C depend on the smoothness parameter). We consider two kings of such fonctional namely functional that is a uniform norm on [0,1] and the functional that is the vaue of function at a given point, belonging to [0,1]. Using the minimax approach, we find the exact value of constant C for these two problems in situation of Hölder classes of functions.

Suggested Citation

  • LEPSKII , Oleg V., 1993. "On Asymptotically Exact Testing of Nonparametric Hypotheses," LIDAM Discussion Papers CORE 1993029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1993029
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