Maximum likelihood estimation of the mixture of log-concave densities

Hu, Hao; Wu, Yichao; Yao, Weixin

doi:10.1016/j.csda.2016.03.002

Cited by 13 publications

(10 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By extending the idea of Hu et al (), Hu et al () proposed a robust EM‐type algorithm for mixture regression models by assuming the component error densities are log‐concave. A density g ( x ) is log‐concave if its log‐density,

ϕ false(x false) = normallog g false(x false)

, is concave.…”

Section: Robust Mixture Regression Methodsmentioning

confidence: 99%

A Selective Overview and Comparison of Robust Mixture Regression Estimators

Yao

Yang

2019

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

Summary Mixture regression models have been widely used in business, marketing and social sciences to model mixed regression relationships arising from a clustered and thus heterogeneous population. The unknown mixture regression parameters are usually estimated by maximum likelihood estimators using the expectation–maximisation algorithm based on the normality assumption of component error density. However, it is well known that the normality‐based maximum likelihood estimation is very sensitive to outliers or heavy‐tailed error distributions. This paper aims to give a selective overview of the recently proposed robust mixture regression methods and compare their performance using simulation studies.

show abstract

ϕ false(x false) = normallog g false(x false)

, is concave.…”

Section: Robust Mixture Regression Methodsmentioning

confidence: 99%

A Selective Overview and Comparison of Robust Mixture Regression Estimators

Yao

Yang

2019

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

show abstract

“…This work largely inspired further work on nonparametric mixture models from the kernel density estimation viewpoint. But nonparametric maximum likelihood estimation is also possible if one assumes log-concavity of the component densities [18].…”

Section: Four Kinds Of Mixture Models 21 a Review Of Paradigms For Mmentioning

confidence: 99%

“…Proof of Theorem 1. In this proof, the symbolp n stands for the solution of the optimization problem (17)- (18), that is, without the positivity constraint, and the symbolp + n stands for the solution of the optimization problem (14)- (15), that is, with the positivity constraint. In view of Lemma 1, it is sufficient to show that…”

Section: A2 Proof Of Theoremmentioning

confidence: 99%

Constraining kernel estimators in semiparametric copula mixture models

Mazo

Averyanov

2019

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

This paper presents a novel algorithm for performing inference and/or clustering in semiparametric copula-based mixture models. The algorithm replaces the standard kernel density estimator by a weighted version that permits to take into account the constraints put on the underlying marginal densities. Lower misclassification error rates and better estimates are obtained on simulations. The pointwise consistency of the weighted kernel density estimator is established under an assumption on the rate of convergence of the sample maximum.

show abstract

“…In the multivariate case, the most popular extensions have been to inflate the tails by using multivariate t ‐kernels (McLachlan and Peel, 1998; Lee and McLachlan, 2016) and/or to generalize the Gaussian distribution to allow skewness (Azzalini and Dalla Valle, 1996; Arellano‐Valle and Azzalini, 2009). Motivated by the problem of more robust clustering, methods are also available for non‐parametrically estimating the kernels subject to unimodality (Rodríguez and Walker, 2014) and log‐concavity (Hu et al ., 2016) restrictions. Also, to improve robustness of clustering, one can use a mixture of mixtures model employing multiple kernels having similar location parameters to characterize the data within a cluster (Malsiner‐Walli et al ., 2017).…”

Section: Introductionmentioning

confidence: 99%

Estimating Densities with Non-Linear Support by Using Fisher–Gaussian Kernels

Mukhopadhyay

Dunson

2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

View full text Add to dashboard Cite

Summary Current tools for multivariate density estimation struggle when the density is concentrated near a non‐linear subspace or manifold. Most approaches require the choice of a kernel, with the multivariate Gaussian kernel by far the most commonly used. Although heavy‐tailed and skewed extensions have been proposed, such kernels cannot capture curvature in the support of the data. This leads to poor performance unless the sample size is very large relative to the dimension of the data. The paper proposes a novel generalization of the Gaussian distribution, which includes an additional curvature parameter. We refer to the proposed class as Fisher–Gaussian kernels, since they arise by sampling from a von Mises–Fisher density on the sphere and adding Gaussian noise. The Fisher–Gaussian density has an analytic form and is amenable to straightforward implementation within Bayesian mixture models by using Markov chain Monte Carlo sampling. We provide theory on large support and illustrate gains relative to competitors in simulated and real data applications.

show abstract

Maximum likelihood estimation of the mixture of log-concave densities

Cited by 13 publications

References 34 publications

A Selective Overview and Comparison of Robust Mixture Regression Estimators

A Selective Overview and Comparison of Robust Mixture Regression Estimators

Constraining kernel estimators in semiparametric copula mixture models

Estimating Densities with Non-Linear Support by Using Fisher–Gaussian Kernels

Contact Info

Product

Resources

About