Publication: Asymptotic normality for the K-phi-divergence goodness-of-fit tests
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In this paper for a wide class of goodness-of-fit statistics based Ko-divergences, the asymptotic normality is established under the assumption n/m(n) --> a is an element of (0, infinity), where m(n) denotes sample size and Mn the number of cells. This result is extended to contiguous alternatives to study asymptotic efficiency.
S.M.Ali, S.D.Silvey, A general class of coefficients of divergence of one distribution from another, J.Roy.Statist. Soc.Ser.B 28 (1966) 131–142. J.Burbea, C.R.Rao, On the convexity of some divergence measures based on entropy functions, IEEE Trans.Inform. Theory 28 (1982) 489–495. N.Cressie, T.R.C.Read, Multinomial goodness-of-&t tests, J.Roy.Statist.Soc.Ser.B 46 (1984) 440–464. I.Csiszar, Information-type measures of difference of probability distributions and indirect observations, Studia Sci.Math.Hungar 2 (1967) 299–318. L.Holst, Asymptotic normality and effciency for certain goodness-of-fit tests, Biometrika 59 (1972) 137–145, 699. G.I. Ivchenko, Y.I. Medvedev, Separable statistics and hypothesis testing, The case of small samples, Theory Probab. Appl.23 (1978) 764–775. M.L. Menéndez, D.Morales, L.Pardo, I.Vajda, Asymptotic distributions of phi-divergences of hypothetical and observed frequencies in sparse testing schemes, Statist.Neerlandica 52 (1) (1998) 71–89. C.Morris, Central limit theorems for multinomial sums, Ann.Statist.3 (1975) 165–188. K.Pearson, On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that can be reasonably supposed to have arisen from random sampling, Philos.Mag.50 (1900)