A Simple Bivariate Example of Fast Convergence Rates for Maximum Likelihood Estimates

Fuente: arXiv
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Main Author: Sarantsev, Andrey
Format: Preprint
Published: 2026
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author Sarantsev, Andrey
author_facet Sarantsev, Andrey
contents We present a one-parameter family of bivariate absolutely continuous distributions based on location-scale family of variance Gaussian mixtures, with continuous densities with the same support (effective domain). The maximum likelihood estimation of the location parameter converges to the true value faster than the classic square root rate. In fact, we can obtain any convergence rate given by a regularly varying function with index greater than 0.5, and some convergence rates given by regularly varying functions with index 0.5 but faster than the classic square root rate.
format Preprint
id arxiv_https___arxiv_org_abs_2605_00198
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Simple Bivariate Example of Fast Convergence Rates for Maximum Likelihood Estimates
Sarantsev, Andrey
Statistics Theory
60E05, 62F10, 62F12
We present a one-parameter family of bivariate absolutely continuous distributions based on location-scale family of variance Gaussian mixtures, with continuous densities with the same support (effective domain). The maximum likelihood estimation of the location parameter converges to the true value faster than the classic square root rate. In fact, we can obtain any convergence rate given by a regularly varying function with index greater than 0.5, and some convergence rates given by regularly varying functions with index 0.5 but faster than the classic square root rate.
title A Simple Bivariate Example of Fast Convergence Rates for Maximum Likelihood Estimates
topic Statistics Theory
60E05, 62F10, 62F12
url https://arxiv.org/abs/2605.00198