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

Fadoua Balabdaoui

Journal of Nonparametric Statistics, 2014, vol. 26, issue 1, 21-59

Abstract: Let X 1 , ..., X n 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 ℓ q distances for q ∈{1, 2, ...}∪{∞}. We also show how these asymptotic results could be used in testing whether a pmf is geometric.

Date: 2014
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DOI: 10.1080/10485252.2013.826801

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