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Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…

Statistics Theory · Mathematics 2013-11-21 Ricardo Maronna , Víctor Yohai

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

Statistics Theory · Mathematics 2022-11-28 Junichiro Yoshida , Nakahiro Yoshida

Triangular distributions are a well-known class of distributions that are often used as elementary example of a probability model. In the past, enumeration and order statistic-based methods have been suggested for the maximum likelihood…

Computation · Statistics 2016-02-16 Hien D Nguyen , Geoffrey J McLachlan

We develop Stein's method for the half-normal distribution and apply it to derive rates of convergence in distributional limit theorems for three statistics of the simple symmetric random walk: the maximum value, the number of returns to…

Probability · Mathematics 2015-11-24 Christian Döbler

Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…

Methodology · Statistics 2015-06-23 Zhong Guan

Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…

Statistics Theory · Mathematics 2017-08-08 Clement Dombry , Sebastian Engelke , Marco Oesting

The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…

Statistics Theory · Mathematics 2016-02-01 Tatiane F. N. Melo , Silvia L. P. Ferrari , Alexandre G. Patriota

Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

Methodology · Statistics 2023-01-25 Anupam Kundu , Mohsen Pourahmadi

A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There…

Statistics Theory · Mathematics 2014-03-13 Mitia Duerinckx , Christophe Ley , Yvik Swan

The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-R\"ollin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. The more general linear regression condition…

Probability · Mathematics 2010-05-18 Elizabeth S. Meckes

In finite mixtures of location-scale distributions, if there is no constraint on the parameters then the maximum likelihood estimate does not exist. But when the ratios of the scale parameters are restricted appropriately, the maximum…

Statistics Theory · Mathematics 2011-11-09 Kentaro Tanaka

Benchmark dose (BMD; a dose associated with a specified change in response) is used to determine the point of departure for the acceptable daily intake of substances for humans. Multiple dose-response relationship models are considered in…

Computation · Statistics 2025-05-13 Sota Minewaki , Tomohiro Ohigashi , Takashi Sozu

One of the most common methods for statistical inference is the maximum likelihood estimator (MLE). The MLE needs to compute the normalization constant in statistical models, and it is often intractable. Using unnormalized statistical…

Statistics Theory · Mathematics 2016-04-26 Takafumi Kanamori , Takashi Takenouchi

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…

We revisit the problem of parameter estimation for discrete probability distributions with values in $\mathbb{Z}^d$. To this end, we adapt a technique called Stein's Method of Moments to discrete distributions which often gives closed-form…

Statistics Theory · Mathematics 2025-10-22 Adrian Fischer

We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…

Probability · Mathematics 2017-12-05 A. D. Barbour , Adrian Röllin , Nathan Ross

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

Probability · Mathematics 2023-04-27 Guillaume Mijoule , Martin Raič , Gesine Reinert , Yvik Swan

In this study, we introduce an innovative methodology aimed at enhancing Fisher's Linear Discriminant Analysis (LDA) in the context of high-dimensional data classification scenarios, specifically addressing situations where each feature…

Applications · Statistics 2024-01-18 Seungyeon Oh , Hoyoung Park

The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory and is in common use for analyzing the far tail of observed phenomena. Curiously, important asymptotic properties of…

Statistics Theory · Mathematics 2020-08-17 Likun Zhang , Benjamin Shaby

In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no…

Computation · Statistics 2017-07-26 Jorge Alberto Achcar , Pedro Luiz Ramos , Edson Zangiacomi Martinez