Bayesian Tobit quantile regression using-prior distribution with ridge parameter

A Bayesian approach is proposed for coefficient estimation in the Tobit quantile regression model. The proposed approach is based on placing a g-prior distribution depends on the quantile level on the regression coefficients. The prior is generalized by introducing a ridge parameter to address important challenges that may arise with censored data, such as multicollinearity and overfitting problems. Then, a stochastic search variable selection approach is proposed for Tobit quantile regression model based on g-prior. An expression for the hyperparameter g is proposed to calibrate the modified g-prior with a ridge parameter to the corresponding g-prior. Some possible extensions of the proposed approach are discussed, including the continuous and binary responses in quantile regression. The methods are illustrated using several simulation studies and a microarray study. The simulation studies and the microarray study indicate that the proposed approach performs well

Fitting censored quantile regression by variable neighborhood search

Quantile regression is an increasingly important topic in statistical analysis. However, fitting censored quantile regression is hard to solve numerically because the objective function to be minimized is not convex nor concave in regressors. Performance of standard methods is not satisfactory, particularly if a high degree of censoring is present. The usual approach is to simplify (linearize) estimator function, and to show theoretically that such approximation converges to optimal values. In this paper, we suggest a new approach, to solve optimization problem (nonlinear, nonconvex, and nondifferentiable) directly. Our method is based on variable neighborhood search approach, a recent successful technique for solving global optimization problems. The presented results indicate that our method can improve quality of censored quantizing regressors estimator considerably

Semiparametric Methods for Clustered Recurrent Event Data

In biomedical studies, the event of interest is often recurrent and within-subject events cannot usually be assumed independent. In addition, individuals within a cluster might not be independent; for example, in multi-center or familial studies, subjects from the same center or family might be correlated. We propose methods of estimating parameters in two semi-parametric proportional rates/means models for clustered recurrent event data. The first model contains a baseline rate function which is common across clusters, while the second model features cluster-specific baseline rates. Dependence structures for patients-within-cluster and events-within-patient are both unspecified. Estimating equations are derived for the regression parameters. For the common baseline model, an estimator of the baseline mean function is proposed. The asymptotic distributions of the model parameters are derived, while finite-sample properties are assessed through a simulation study. Using data from a national organ failure registry, the proposed methods are applied to the analysis of technique failures among Canadian dialysis patients.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46817/1/10985_2005_Article_2970.pd

Simple resampling methods for censored regression quantiles

Powell (Journal of Econometrics 25 (1984) 303-325; journal of Econometrics 32 (1986) 143-155) considered censored regression quantile estimators. The asymptotic covariance matrices of his estimators depend on the error densities and are therefore difficult to estimate reliably. The difficulty may be avoided by applying the bootstrap method (Hahn, Econometric Theory 11 (1995) 105-121). Calculation of the estimators, however, requires solving a nonsmooth and nonconvex minimization problem, resulting in high computational costs in implementing the bootstrap, We propose in this paper computationally simple resampling methods by convexfying Powell's approach in the resampling stage. A major advantage of the new methods is that they can be implemented by efficient linear programming. Simulation studies show that the methods are reliable even with moderate sample sizes. (C) 2000 Elsevier Science S.A. All rights reserved. JEL classification: C14; C24