On distance-type Gaussian estimation
type: Item
instance of: scholarly article
title: On distance-type Gaussian estimation
author: Elena Castilla
author: K. Zografos
published in: Journal of Multivariate Analysis
publication date: 2022-01-03T00:00:00Z
review text: Maximum likelihood estimation method is a popular and simple method to estimate the parameters of a model. However, there are cases where this method cannot be applied or is not recommended to be applied. For instance, this method cannot be applied when the model, which describes the data, is intractable or when it contains intractable normalizing constant which is a function of the unknown population parameters. Moreover, since maximum likelihood estimation is highly affected by the presence of outliers in the data, it is not recommended to be applied in such cases. To overcome the first problem, \textit{T. Zhang} [J. Multivariate Anal. 169, 234--247 (2019; Zbl 1433.62080)] proposed, under the assumption that the computation of the population mean vector \(\mu\) and the population covariance matrix \(\Sigma\) is not so arduous, the replacement of the initial intractable model by the normal model. This approach is called general Gaussian estimation. On the other hand, minimum distance estimation methods can be used in order to tackle the presence of outliers, since these methods are characterized by good efficiency and robustness properties. Among the existing minimum distance estimation methods, the Minimum density power divergence (DPD) estimation method, introduced by \textit{A. Basu} et al. [Biometrika 85, No. 3, 549--559 (1998; Zbl 0926.62021)], has a prominent position. In this paper, which consists of eight sections, a new procedure for estimating the parameters of a model is proposed by combining Zhang's Gaussian estimation approach [\textit{T. Zhang}, J. Multivariate Anal. 169, 234--247 (2019; Zbl 1433.62080)] and the minimum density power divergence estimators of \textit{A. Basu} et al. [Biometrika 85, No. 3, 549--559 (1998; Zbl 0926.62021)]. In this context, after an excellent introduction which gives clearly the motivation of the current work (Section 1), the Minimum DPD Gaussian estimation (MDPDGE) method is introduced in Section 2 of the paper. The con…
reviewed by: A. Batsidis
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 7451352
zbMATH Keywords: density power divergence
zbMATH Keywords: elliptically contoured distributions
zbMATH Keywords: Gaussian estimation
zbMATH Keywords: maximum likelihood estimation
zbMATH Keywords: minimum density power divergence Gaussian estimation
zbMATH Keywords: robustness
MaRDI profile type: Publication
full work available at URL: j.jmva.2021.104831
OpenAlex ID: W3200668497
cites work: Q4420195
cites work: Maximum-likelihood estimates and likelihood-ratio criteria for multivariate elliptically contoured distributions
cites work: Robust Wald-type tests for non-homogeneous observations based on the minimum density power divergence estimator
cites work: Robust and efficient estimation by minimising a density power divergence
cites work: Generalized Wald-type tests based on minimum density power divergence estimators
cites work: Statistical Inference
cites work: The emperor's new clothes: a critique of the multivariate t regression model
cites work: Composite likelihood methods: Rao-type tests based on composite minimum density power divergence estimator
cites work: Elements of Information Theory
cites work: Q3996150
cites work: Q3999358
cites work: Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression
cites work: Ultrahigh-Dimensional Robust and Efficient Sparse Regression Using Non-Concave Penalized Density Power Divergence
cites work: A multivariate generalization of the power exponential family of distributions
cites work: Information Theory and Statistical Mechanics
cites work: Q5326868
cites work: Q5179661
cites work: Some extremal type elliptical distributions
cites work: Multivariate T-Distributions and Their Applications
cites work: On the difference in inference and prediction between the joint and independent f-error models for seemingly unrelated regressions
cites work: Q5702553
cites work: Flexible linear mixed models with improper priors for longitudinal and survival data
cites work: Choosing a robustness tuning parameter
cites work: General Gaussian estimation
cites work: On maximum entropy characterization of Pearson's type II and VII multivariate distributions
DOI: 10.1016/J.JMVA.2021.104831
Recommended article: Q3764394
Recommended article: Estimation of distance functionals between density functions
Recommended article: Q4006545
Recommended article: Q3626467
Recommended article: A Wasserstein-Type Distance in the Space of Gaussian Mixture Models
Recommended article: Statistical properties of distance estimators
Recommended article: Gromov–Wasserstein distances between Gaussian distributions
Recommended article: On parameter estimation with the Wasserstein distance
description: scientific article; zbMATH DE number 7451352