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Literature DB >> 28966409

GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES.

Abstract

We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and s-concave densities on ℝ. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than n-2/5 when -1 < s < ∞ where s = 0 corresponds to the log-concave case. We also show that the MLE does not exist for the classes of s-concave densities with s < -1.

Entities: Chemical Disease Gene

Keywords: Bracketing entropy; Hellinger metric; Primary 62G07; consistency; empirical processes; global rate; log-concave; s-concave; secondary 62G05, 62G20

Year: 2016 PMID： 28966409 PMCID： PMC5619328 DOI： 10.1214/15-AOS1394

Source DB: PubMed Journal: Ann Stat ISSN： 0090-5364 Impact factor: 4.028

4 in total

3 in total

GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES.

1. NONPARAMETRIC ESTIMATION OF MULTIVARIATE CONVEX-TRANSFORMED DENSITIES.

2. Limit Distribution Theory for Maximum Likelihood Estimation of a Log-Concave Density.

3. APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RÉNYI DIVERGENCES.

4. GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES.

1. Maximum likelihood estimation of the mixture of log-concave densities.

2. APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RÉNYI DIVERGENCES.

3. GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES.