On distinguishability of two nonparametric sets of hypothesis

M. S. Ermakov

Statistics & Probability Letters, 2000, vol. 48, issue 3, 275-282

Abstract: Let we observe a signal S(t), t[set membership, variant](0,1) in Gaussian white noise [var epsilon] dw(t). The problem is to test a hypothesis S[set membership, variant][Theta]1[subset of]L2(0,1) versus alternatives S[set membership, variant][Theta]2[subset of]L2(0,1). The sets [Theta]1,[Theta]2 are closed and bounded. We show that there exists a statistical procedure allowing to make a true solution S[set membership, variant][Theta]1 or S[set membership, variant][Theta]2 with probability tending to one as [var epsilon]-->0 (i.e. to distinguish two nonparametric sets [Theta]1 and [Theta]2) iff there exists a finite-dimensional subspace H[subset of]L2(0,1) such that the projections [Theta]1 and [Theta]2 on H have no common points. A similar result is also obtained for the problems of testing hypotheses about density.

Keywords: Hypothesis; testing; Asymptotic; efficiency; Signal; detection; Hypothesis; testing; about; density; Nonparametric; hypothesis; testing (search for similar items in EconPapers)
Date: 2000
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