Global convergence of the log-concave MLE when the true distribution is geometric

Balabdaoui, Fadoua

Balabdaoui, Fadoua (2014), Global convergence of the log-concave MLE when the true distribution is geometric, Journal of Nonparametric Statistics, 26, 1, p. 21-59. http://dx.doi.org/10.1080/10485252.2013.826801

Type

Article accepté pour publication ou publié

Date

2014

Journal name

Journal of Nonparametric Statistics

Volume

Number

Publisher

Taylor & Francis

Pages

21-59

Abstract (EN)

Let X1, …, Xn be i.i.d. from a discrete probability mass function (pmf) p. In Balabdaoui et al. [(2013), ‘Asymptotic Distribution of the Discrete Log-Concave mle and Some Applications’, JRSS-B, in press], the pointwise limit distribution of the log-concave maximum-likelihood estimator (MLE) was derived in both the well- and misspecified settings. In the well-specified setting, the geometric distribution was excluded, classified as being degenerate. In this article, we establish the global asymptotic theory of the log-concave MLE of a geometric pmf in all ℓq distances for q{1, 2, …}{∞}. We also show how these asymptotic results could be used in testing whether a pmf is geometric.

Subjects / Keywords

Borel–Cantelli; geometric distribution; global convergence; goodness of fit; log-concave; maximum likelihood; PMF