Penalized empirical likelihood for quantile regression with missing covariates and auxiliary information

Based on the inverse probability weight method, we, in this article, construct the empirical likelihood (EL) and penalized empirical likelihood (PEL) ratios of the parameter in the linear quantile regression model when the covariates are missing at random, in the presence and absence of auxiliary information, respectively. It is proved that the EL ratio admits a limiting Chi-square distribution. At the same time, the asymptotic normality of the maximum EL and PEL estimators of the parameter is established. Also, the variable selection of the model in the presence and absence of auxiliary information, respectively, is discussed. Simulation study and a real data analysis are done to evaluate the performance of the proposed methods.     

Marginalized lasso in sparse regression

We propose marginalized lasso, a new nonconvex penalization for variable selection in regression problem. The marginalized lasso penalty is motivated from integrating out the penalty parameter in the original lasso penalty with a gamma prior distribution. This study provides a thresholding rule and a lasso-based iterative algorithm for parameter estimation in the marginalized lasso. We also provide a coordinate descent algorithm to efficiently optimize the marginalized lasso penalized regression. Numerical comparison studies are provided to demonstrate its competitiveness over the existing sparsity-inducing penalizations and suggest some guideline for tuning parameter selection.     

Bayesian estimation on semiparametric models with shape restricted B-splines

In this paper, we develop a Bayesian estimation procedure for semiparametric models under shape constrains. The approach uses a hierarchical Bayes framework and characterizations of shape-constrained B-splines. We employ Markov chain Monte Carlo methods for model fitting, using a truncated normal distribution as the prior for the coefficients of basis functions to ensure the desired shape constraints. The small sample properties of the function estimators are provided via simulation and compared with existing methods. A real data analysis is conducted to illustrate the application of the proposed method.     

Properties of maximum likelihood estimators of variance components in the one-way classification,balanced data

We studied properties of maximum likelihood estimators (MLEs) of the variance components obtained from balanced data of the one-way classification. Exact and asymptotic expected values and variances of these MLEs were derived under the usual normality assumptions. Numerical studies illustrate these expected values and variances, and also illustrate the probability of obtaining a negative solution to the maximum likelihood (ML) equation for the between-class variance component. Simulations were used to study the robustness of the ML estimators under non-normal distributions.     

Finite Mixture of Generalized Semiparametric Models: Variable Selection via Penalized Estimation

Selection of the important variables is one of the most important model selection problems in statistical applications. In this article, we address variable selection in finite mixture of generalized semiparametric models. To overcome computational burden, we introduce a class of variable selection procedures for finite mixture of generalized semiparametric models using penalized approach for variable selection. Estimation of nonparametric component will be done via multivariate kernel regression. It is shown that the new method is consistent for variable selection and the performance of proposed method will be assessed via simulation.     

Bias in Multinomial Models

This paper investigates bias in parameter estimates and residual diagnostics for parametric multinomial models by considering the effect of deleting a cell. In particular, it describes the average changes in the standardized residuals and maximum likelihood estimates resulting from conditioning on the given cells. These changes suggest how individual cell observations affect biases. Emphasis is placed on the role of individual cell observations in determining bias and on how bias affects standard diagnostic methods. Examples from genetics and log–linear models are considered. Numerical results show that conditioning on an influential cell results in substantial changes in biases.     

A Flexible Method for Estimating the ROC Curve

In this paper we propose a flexible method for estimating a receiver operating characteristic (ROC) curve that is based on a continuous-scale test. The approach is easily understood and efficiently computed, and robust to the smooth parameter selection, which needs intensive computation when using local polynomial and smoothing spline techniques. The results from our simulation experiment indicate that the moderate-sample numerical performance of our estimator is better than the empirical ROC curve estimator and comparable to the local linear estimator. The availability of easy implementation is also illustrated by our simulation. We apply the proposed method to two real data sets.     

Tuning Parameter Selection in Penalized Frailty Models

The penalized likelihood approach of Fan and Li (2001 Fan, J., Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Association 96:1348–1360.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 2002 Fan, J., Li, R. (2002). Variable selection for Cox’s proportional hazards model and frailty model. The Annals of Statistics 30:74–99.[Crossref], [Web of Science ®] , [Google Scholar]) differs from the traditional variable selection procedures in that it deletes the non-significant variables by estimating their coefficients as zero. Nevertheless, the desirable performance of this shrinkage methodology relies heavily on an appropriate selection of the tuning parameter which is involved in the penalty functions. In this work, new estimates of the norm of the error are firstly proposed through the use of Kantorovich inequalities and, subsequently, applied to the frailty models framework. These estimates are used in order to derive a tuning parameter selection procedure for penalized frailty models and clustered data. In contrast with the standard methods, the proposed approach does not depend on resampling and therefore results in a considerable gain in computational time. Moreover, it produces improved results. Simulation studies are presented to support theoretical findings and two real medical data sets are analyzed.     

Collinearity in generalized linear regression

The problem of ill-conditioning in generalized linear regression is investigated. Besides collinearity among the explanatory variables, we define another type of ill-conditioning, namely ML-collinearity, which has similar detrimental effects on the covariance matrix, e.g. inflation of some of the estimated standard errors of the regression coefficients. For either situation there is collinearity among the columns of the matrix of the weighted variables. We present both methods to detect, as well as practical examples to illustrate, the difference between these two types of ill-conditioning. Also the applicability of alternative regression methods will be reviewed.     

Penalized pseudo-likelihood hazard estimation: A fast alternative to penalized likelihood

Penalized likelihood method has been developed previously for hazard function estimation using standard left-truncated, right-censored lifetime data with covariates, and the functional ANOVA structures built into the log hazard allows for versatile nonparametric modeling in the setting. The computation of the method can be time-consuming in the presence of continuous covariates; however, due to the repeated numerical integrations involved. Adapting a device developed by Jeon and Lin [An effective method for high dimensional log-density ANOVA estimation, with application to nonparametric graphical model building. Statist. Sinica 16, 353–374] for penalized likelihood density estimation, we explore an alternative approach to hazard estimation where the log likelihood is replaced by some computationally less demanding pseudo-likelihood. An assortment of issues are addressed concerning the practical implementations of the approach including the selection of smoothing parameters, and extensive simulations are presented to assess the inferential efficiency of the “pseudo” method as compared to the “real” one. Also noted is an asymptotic theory concerning the convergence rates of the estimates parallel to that for the original penalized likelihood estimation.