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Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models

✍ Scribed by L. Györfi; I. Vajda

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
130 KB
Volume
56
Category
Article
ISSN
0167-7152

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✦ Synopsis

We consider f-disparities D f ( pn ; p n ) between discrete distributions p n = (p n1 ; : : : ; p nkn ) and their estimates pn = ( pn1 ; : : : ; pnkn ) based on relative frequencies in an i.i.d. sample of size n, where f : (0; ∞) → R is twice continuously di erentiable in a neighborhood of 1 with f (1) = 0. We derive asymptotic distributions of the disparity statistics n D f ( pn ; p n ) under certain assumptions about p n and the second derivatives f in a neighborhood of 1. These assumptions are weaker than those known from the literature.

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