Saddlepoint Approximation for Data in Simplices: A Review with New Applications

Riccardo Gatto
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Riccardo Gatto: Institute of Mathematical Statistics and Actuarial Science, University of Bern, 3012 Bern, Switzerland

Stats, 2019, vol. 2, issue 1, 1-27

Abstract: This article provides a review of the saddlepoint approximation for a M-statistic of a sample of nonnegative random variables with fixed sum. The sample vector follows the multinomial, the multivariate hypergeometric, the multivariate Polya or the Dirichlet distributions. The main objective is to provide a complete presentation in terms of a single and unambiguous notation of the common mathematical framework of these four situations: the simplex sample space and the underlying general urn model. Some important applications are reviewed and special attention is given to recent applications to models of circular data. Some novel applications are developed and studied numerically.

Keywords: bootstrap; circular data; Dirichlet distribution; entropy; likelihood ratio test; multinomial distribution; multivariate hypergeometric distribution; multivariate Polya distribution; spacings; spacing-frequencies; urn model (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:2:y:2019:i:1:p:10-147:d:207013

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