3 research outputs found

    Robust multivariate mixture regression models with incomplete data

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    <p>Multivariate mixture regression models can be used to investigate the relationships between two or more response variables and a set of predictor variables by taking into consideration unobserved population heterogeneity. It is common to take multivariate normal distributions as mixing components, but this mixing model is sensitive to heavy-tailed errors and outliers. Although normal mixture models can approximate any distribution in principle, the number of components needed to account for heavy-tailed distributions can be very large. Mixture regression models based on the multivariate <i>t</i> distributions can be considered as a robust alternative approach. Missing data are inevitable in many situations and parameter estimates could be biased if the missing values are not handled properly. In this paper, we propose a multivariate <i>t</i> mixture regression model with missing information to model heterogeneity in regression function in the presence of outliers and missing values. Along with the robust parameter estimation, our proposed method can be used for (i) visualization of the partial correlation between response variables across latent classes and heterogeneous regressions, and (ii) outlier detection and robust clustering even under the presence of missing values. We also propose a multivariate <i>t</i> mixture regression model using MM-estimation with missing information that is robust to high-leverage outliers. The proposed methodologies are illustrated through simulation studies and real data analysis.</p

    Skinny Gibbs: A Consistent and Scalable Gibbs Sampler for Model Selection

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    <p>We consider the computational and statistical issues for high-dimensional Bayesian model selection under the Gaussian spike and slab priors. To avoid large matrix computations needed in a standard Gibbs sampler, we propose a novel Gibbs sampler called “Skinny Gibbs” which is much more scalable to high-dimensional problems, both in memory and in computational efficiency. In particular, its computational complexity grows only linearly in <i>p</i>, the number of predictors, while retaining the property of strong model selection consistency even when <i>p</i> is much greater than the sample size <i>n</i>. The present article focuses on logistic regression due to its broad applicability as a representative member of the generalized linear models. We compare our proposed method with several leading variable selection methods through a simulation study to show that Skinny Gibbs has a strong performance as indicated by our theoretical work. Supplementary materials for this article are available online.</p

    A New Approach to Censored Quantile Regression Estimation<sup>*</sup>

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    <p>Quantile regression provides an attractive tool to the analysis of censored responses, because the conditional quantile functions are often of direct interest in regression analysis, and moreover, the quantiles are often identifiable while the conditional mean functions are not. Existing methods of estimation for censored quantiles are mostly limited to singly left- or right-censored data, with some attempts made to extend the methods to doubly-censored data. In this article we propose a new and unified approach, based on a variation of the data augmentation algorithm, to censored quantile regression estimation. The proposed method adapts easily to different forms of censoring including doubly censored and interval censored data, and somewhat surprisingly, the resulting estimates improve on the performance of the best known estimators with singly censored data.</p
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