Statistical Inference Based on Pseudo-Maximum Likelihood Estimators in Elliptical Populations

Kano, Yutaka; Berkane, Maia; Bentler, Peter M.

doi:10.1080/01621459.1993.10594303

Cited by 43 publications

(27 citation statements)

References 34 publications

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“…A subject of further study would be to consider the possibility that the adopted elliptical model is not correctly specified. One such study developed in Kano et al (1993) treats the case of ordinary elliptical models.…”

Section: Final Conclusionmentioning

confidence: 99%

“…An special situation not also solved and often considered in the literature (Bolfarine and Galea-Rojas, 1995) assumes that Var[= i ]=_ 2 I p , where I p is the identity matrix of dimension p and _ 2 is unknown. One way to counter this problem would be to consider a pseudo-likelihood approach (Gong and Samaniego, 1981;Kano et al, 1993), where the unknown _ 2 is replaced by a consistent estimator. This approach may lead to some efficiency loss in the estimation of ;.…”

Section: Final Conclusionmentioning

confidence: 99%

See 1 more Smart Citation

Elliptical Functional Models

Vilca

Arellano–Valle

Bolfarine

1998

Journal of Multivariate Analysis

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In this paper, functional models with not replications are investigated within the class of the elliptical distributions. Emphasis is placed on the special case of the Student-t distribution. Main results encompasses consistency and asymptotic normality of the maximum likelihood estimators. Due to the presence of incidental parameters, standard maximum likelihood methodology cannot be used to obtain the main results, which require extensions of some existing results related to elliptical distributions. Asymptotic relative efficiencies are reported which show that the generalized least squares estimator can be highly inefficient when compared with the maximum likelihood estimator under nonnormality.1998 Academic Press AMS 1990 subject classifications: 62F05, 62J05.

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Section: Final Conclusionmentioning

confidence: 99%

Section: Final Conclusionmentioning

confidence: 99%

Elliptical Functional Models

Vilca

Arellano–Valle

Bolfarine

1998

Journal of Multivariate Analysis

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“…As violation of this assumption would lead to misleading inferences on observed and latent variable distributions, and sometimes even lead to bad effects on the estimation of the parameters, development of robust methods for analyzing non-normal data has received a great deal of attention in SEMs. Methods developed with parametric distributions that are related to the multivariate t-distribution have been proposed for handling non-normal data with symmetrically heavy tails (see, for example, Bentler, 1983;Shapiro and Browne, 1987;Kano, Berkane, and Bentler, 1993;Lee and Xia, 2006;among others). Statistical inference using the t-distribution mentioned above is parametric.…”

Section: Introductionmentioning

confidence: 99%

A semiparametric Bayesian approach for structural equation models

et al. 2010

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In the development of structural equation models (SEMs), observed variables are usually assumed to be normally distributed. However, this assumption is likely to be violated in many practical researches. As the non-normality of observed variables in an SEM can be obtained from either non-normal latent variables or non-normal residuals or both, semiparametric modeling with unknown distribution of latent variables or unknown distribution of residuals is needed. In this article, we find that an SEM becomes nonidentifiable when both the latent variable distribution and the residual distribution are unknown. Hence, it is impossible to estimate reliably both the latent variable distribution and the residual distribution without parametric assumptions on one or the other. We also find that the residuals in the measurement equation are more sensitive to the normality assumption than the latent variables, and the negative impact on the estimation of parameters and distributions due to the non-normality of residuals is more serious. Therefore, when there is no prior knowledge about parametric distributions for either the latent variables or the residuals, we recommend making parametric assumption on latent variables, and modeling residuals nonparametrically. We propose a semiparametric Bayesian approach using the truncated Dirichlet process with a stick breaking prior to tackle the non-normality of residuals in the measurement equation. Simulation studies and a real data analysis demonstrate our findings, and reveal the empirical performance of the proposed methodology. A free WinBUGS code to perform the analysis is available in Supporting Information.

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“…However, most of these methods are mainly developed within particular parametric distribution families such as the exponential family or normal scale mixture family, which have a limited role in dealing with the distributional deviations, in particular heterogeneity or multimodality of the data. Though some robust methods are developed to downweight the influence of the outliers [7][8][9][10][11][12], most of them are still confined to dealing with unimodality and are less effective for the asymmetric and/or multimodal problems.…”

Section: Introductionmentioning

confidence: 99%

Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes

Xia

Gou

2016

Journal of Applied Mathematics

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Factor analysis models with continuous and ordinal responses are a useful tool for assessing relations between the latent variables and mixed observed responses. These models have been successfully applied to many different fields, including behavioral, educational, and social-psychological sciences. However, within the Bayesian analysis framework, most developments are constrained within parametric families, of which the particular distributions are specified for the parameters of interest. This leads to difficulty in dealing with outliers and/or distribution deviations. In this paper, we propose a Bayesian semiparametric modeling for factor analysis model with continuous and ordinal variables. A truncated stick-breaking prior is used to model the distributions of the intercept and/or covariance structural parameters. Bayesian posterior analysis is carried out through the simulation-based method. Blocked Gibbs sampler is implemented to draw observations from the complicated posterior. For model selection, the logarithm of pseudomarginal likelihood is developed to compare the competing models. Empirical results are presented to illustrate the application of the methodology.

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Statistical Inference Based on Pseudo-Maximum Likelihood Estimators in Elliptical Populations

Cited by 43 publications

References 34 publications

Elliptical Functional Models

Elliptical Functional Models

A semiparametric Bayesian approach for structural equation models

Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes

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