Asymptotic distributions of φ-divergences of hypothetical and observed frequencies on refined partitions |
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| Authors: | M. L. Mené ndez,D. Morales,L. Pardo,& I. Vajda |
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| Affiliation: | Department of Applied Mathematics, Technical University of Madrid, Madrid, 28040 Madrid, Spain,;Department of Statistics and Operation Research, Complutense University of Madrid, 28040 Madrid, Spain,;Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, 18208 Prague, Czech Republic |
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| Abstract: | For a wide class of goodness-of-fit statistics based on φ-divergences between hypothetical cell probabilities and observed relative frequencies, the asymptotic normality is established under the assumption n / m n →γ∈(0,∞), where n denotes sample size and m n the number of cells. Related problems of asymptotic distributions of φ-divergence errors, and of φ-divergence deviations of histogram estimators from their expected values, are considered too. |
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| Keywords: | goodness-of-fit sparse testing schemes histogram estimates divergence errors L p -errors asymptotic distributions |
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