Estimation of exponential-polynomial distribution by holonomic gradient descent

Jumpei Hayakawa and Akimichi Takemura

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 23, 6860-6882

Abstract: We study the holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of the distribution is the set of positive reals. We show that the maximum likelihood estimate (MLE) can be easily computed by the holonomic gradient descent, even though the normalizing constant of this family does not have a closed-form expression, and discuss the determination of the degree of the polynomial based on the score test statistic. Then, we present extensions to the whole real line and to the bivariate distribution on the positive orthant.

Date: 2016
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DOI: 10.1080/03610926.2014.968735

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