Small Sample Asymptotics

Author : Ximing Wu
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (129 download)

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Download or read book Information-Theoretic Approximation of Small Sample Distributions written by Ximing Wu and published by . This book was released on 2006 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a simple approach for approximating small sample distributions based on the method of minimum relative entropy density. Unlike previous studies that use this method as a curve-fitting tool, we focus on the 'small sample asymptotics' of the approximation to distributions of general statistics. We show that this method obtains not only the same asymptotic order of accuracy as that of the classical Edgeworth expansion and the exponential Edgeworth expansion by Field and Hampel (1982), but also the minimum Kullback-Leibler distance among all approximations of the same exponential family. The formulation of the minimum relative entropy density facilitates incorporating prior information through a reference density. Moreover, the introduction of a reference density frees us from the assumption of a bounded support, which is typically used in the existing literature. We discuss the selection of a proper reference density that ensures the integrability of the approximation on the real line under various moment constraints. Our numerical experiments show that the proposed method compares competitively with and often outperforms the Edgeworth and exponential Edgeworth expansions, especially when the sample size is small.