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

Institute of Mathematical Statistics and Actuarial Science, University of Bern, 3012 Bern, Switzerland
Stats 2019, 2(1), 121-147; https://doi.org/10.3390/stats2010010
Received: 23 January 2019 / Revised: 8 February 2019 / Accepted: 14 February 2019 / Published: 18 February 2019
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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. View Full-Text
Keywords: bootstrap; circular data; Dirichlet distribution; entropy; likelihood ratio test; multinomial distribution; multivariate hypergeometric distribution; multivariate Polya distribution; spacings; spacing-frequencies; urn model bootstrap; circular data; Dirichlet distribution; entropy; likelihood ratio test; multinomial distribution; multivariate hypergeometric distribution; multivariate Polya distribution; spacings; spacing-frequencies; urn model
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Gatto, R. Saddlepoint Approximation for Data in Simplices: A Review with New Applications. Stats 2019, 2, 121-147.

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