Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(2): 351-363

Printed March 31, 2016

https://doi.org/10.4134/BKMS.2016.53.2.351

Copyright © The Korean Mathematical Society.

Entropy-based goodness of fit test for a composite hypothesis

Sangyeol Lee

Seoul National University

Abstract

In this paper, we consider the entropy-based goodness of fit test (Vasicek's test) for a composite hypothesis. The test measures the discrepancy between the nonparametric entropy estimate and the parametric entropy estimate obtained from an assumed parametric family of distributions. It is shown that the proposed test is asymptotically normal under regularity conditions, but is affected by parameter estimates. As a remedy, a bootstrap version of Vasicek's test is proposed. Simulation results are provided for illustration.

Keywords: goodness of fit test, entropy test, Vasicek's test, composite hypothesis test, bootstrap test

MSC numbers: 62G05, 62G20

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