Semiparametric quantile regression with random censoring

This paper considers estimation and inference in semiparametric quantile regression models when the response variable is subject to random censoring. The paper considers both the cases of independent and dependent censoring and proposes three iterative estimators based on inverse probability weighting, where the weights are estimated from the censoring distribution using the Kaplan–Meier, a fully parametric and the conditional Kaplan–Meier estimators. The paper proposes a computationally simple resampling technique that can be used to approximate the finite sample distribution of the parametric estimator. The paper also considers inference for both the parametric and nonparametric components of the quantile regression model. Monte Carlo simulations show that the proposed estimators and test statistics have good finite sample properties. Finally, the paper contains a real data application, which illustrates the usefulness of the proposed methods.

     

Varying coefficients partially linear models with randomly censored data

This paper considers the problem of estimation and inference in semiparametric varying coefficients partially linear models when the response variable is subject to random censoring. The paper proposes an estimator based on combining inverse probability of censoring weighting and profile least squares estimation. The resulting estimator is shown to be asymptotically normal. The paper also proposes a number of test statistics that can be used to test linear restrictions on both the parametric and nonparametric components. Finally, the paper considers the important issue of correct specification and proposes a nonsmoothing test based on a Cramer von Mises type of statistic, which does not suffer from the curse of dimensionality, nor requires multidimensional integration. Monte Carlo simulations illustrate the finite sample properties of the estimator and test statistics.     

Semiparametric random coefficient regression models

Linear regression models with random coefficients express the idea that each individual sampled may have a different linear response function. Technically speaking, random coefficient regression encompasses a rich variety of submodels. These include deconvolution or affine-mixture models as well as certain classical linear regression models that have heteroscedastic errors, or errors-in-variables, or random effects. This paper studies minimum distance estimates for the coefficient distributions in a general, semiparametric, random coefficient regression model. The analysis yields goodness-of-fit tests for the semiparametric model, prediction regions for future responses, and confidence regions for the distribution of the random coefficients.This research was supported in part by NSF Grant DMS 9001710.     

Weighted composite quantile estimation and variable selection method for censored regression model

This paper considers the weighted composite quantile (WCQ) regression for linear model with random censoring. The adaptive penalized procedure for variable selection in this model is proposed, and the consistency, asymptotic normality and oracle property of the resulting estimators are also derived. The simulation studies and the analysis of an acute myocardial infarction data set are conducted to illustrate the finite sample performance of the proposed method.     

Empirical likelihood inference for censored median regression with weighted empirical hazard functions

In recent years, median regression models have been shown to be useful for analyzing a variety of censored survival data in clinical trials. For inference on the regression parameter, there have been a variety of semiparametric procedures. However, the accuracy of such procedures in terms of coverage probability can be quite low when the censoring rate is heavy. In this paper, based on weighted empirical hazard functions, we apply an empirical likelihood (EL) ratio method to the median regression model with censoring data and derive the limiting distribution of EL ratio. Confidence region for the regression parameter can then be obtained accordingly. Furthermore, we compared the proposed method with the standard method through extensive simulation studies. The proposed method almost always outperformed the existing method.     

Estimation in semiparametric models with missing data

This paper considers the problem of parameter estimation in a general class of semiparametric models when observations are subject to missingness at random. The semiparametric models allow for estimating functions that are non-smooth with respect to the parameter. We propose a nonparametric imputation method for the missing values, which then leads to imputed estimating equations for the finite dimensional parameter of interest. The asymptotic normality of the parameter estimator is proved in a general setting, and is investigated in detail for a number of specific semiparametric models. Finally, we study the small sample performance of the proposed estimator via simulations.     

Semiparametric mixtures of regressions with single-index for model based clustering

In this article, we propose two classes of semiparametric mixture regression models with single-index for model based clustering. Unlike many semiparametric/nonparametric mixture regression models that can only be applied to low dimensional predictors, the new semiparametric models can easily incorporate high dimensional predictors into the nonparametric components. The proposed models are very general, and many of the recently proposed semiparametric/nonparametric mixture regression models are indeed special cases of the new models. Backfitting estimates and the corresponding modified EM algorithms are proposed to achieve optimal convergence rates for both parametric and nonparametric parts. We establish the identifiability results of the proposed two models and investigate the asymptotic properties of the proposed estimation procedures. Simulation studies are conducted to demonstrate the finite sample performance of the proposed models. Two real data applications using the new models reveal some interesting findings.

     

Mixtures of semiparametric varying coefficient models for longitudinal data with nonignorable dropout

Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coefficients depend on the dropout time in a non-parametric way. The local linear version of the profile-kernel method is used to estimate the parameters of the model. The proposed estimators are shown to be consistent and asymptotically normal, and the finite performance of the estimators is evaluated by numerical simulation.     

删失数据中删失指标随机缺失下回归函数的非参数估计

本文在删失数据中删失指标随机缺失的情况下,运用非参数方法给出了回归函数的两种估计量,给出了估计量的一致收敛速度以及渐近分布,并进一步通过数值模拟验证了所提方法在有限样本下的性质.     

Estimation in partially linear models with missing responses at random

A partially linear model is considered when the responses are missing at random. Imputation, semiparametric regression surrogate and inverse marginal probability weighted approaches are developed to estimate the regression coefficients and the nonparametric function, respectively. All the proposed estimators for the regression coefficients are shown to be asymptotically normal, and the estimators for the nonparametric function are proved to converge at an optimal rate. A simulation study is conducted to compare the finite sample behavior of the proposed estimators.     

半参数非线性模型的统计诊断与影响分析

本文系统研究了半参数非线性回归模型的统计诊断与影响分析方法;得到了一系列诊断统计量,两个实际数值例子验证了本文给出的诊断方法的有效性。     

Variable selection for semiparametric varying-coefficient partially linear models with missing response at random

In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.     

Iterative weighted partial spline least squares estimation in semiparametric modeling of longitudinal data

In this paper we consider the estimating problem of a semiparametric regression modelling whenthe data are longitudinal.An iterative weighted partial spline least squares estimator(IWPSLSE)for the para-metric component is proposed which is more efficient than the weighted partial spline least squares estimator(WPSLSE)with weights constructed by using the within-group partial spline least squares residuals in the sense     

Posterior Simulation in the Generalized Linear Mixed Model With Semiparametric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model with normal base measure, Gibbs samplingalgorithms based on the Pólya urn scheme are often used to simulate posterior draws in conjugate models (essentially, linear regression models and models for binary outcomes). In the nonconjugate case, some common problems associated with existing simulation algorithms include convergence and mixing difficulties.

This article proposes an algorithm for MDP models with exponential family likelihoods and normal base measures. The algorithm proceeds by making a Laplace approximation to the likelihood function, thereby matching the proposal with that of the Gibbs sampler. The proposal is accepted or rejected via a Metropolis-Hastings step. For conjugate MDP models, the algorithm is identical to the Gibbs sampler. The performance of the technique is investigated using a Poisson regression model with semi-parametric random effects. The algorithm performs efficiently and reliably, even in problems where large-sample results do not guarantee the success of the Laplace approximation. This is demonstrated by a simulation study where most of the count data consist of small numbers. The technique is associated with substantial benefits relative to existing methods, both in terms of convergence properties and computational cost.     

The quantile process under random censoring

In this paper we discuss the asymptotic properties of quantile processes under random censoring. In contrast to most work in this area we prove weak convergence of an appropriately standardized quantile process under the assumption that the quantile regression model is only linear in the region, where the process is investigated. Additionally, we also discuss properties of the quantile process in sparse regression models including quantile processes obtained from the Lasso and adaptive Lasso. The results are derived by a combination of modern empirical process theory, classical martingale methods and a recent result of Kato (2009).     

Functional inference in semiparametric models using the piggyback bootstrap

This paper introduces the “piggyback bootstrap.” Like the weighted bootstrap, this bootstrap procedure can be used to generate random draws that approximate the joint sampling distribution of the parametric and nonparametric maximum likelihood estimators in various semiparametric models, but the dimension of the maximization problem for each bootstrapped likelihood is smaller. This reduction results in significant computational savings in comparison to the weighted bootstrap. The procedure can be stated quite simply. First obtain a valid random draw for the parametric component of the model. Then take the draw for the nonparametric component to be the maximizer of the weighted bootstrap likelihood with the parametric component fixed at the parametric draw. We prove the procedure is valid for a class of semiparametric models that includes frailty regression models airsing in survival analysis and biased sampling models that have application to vaccine efficacy trials. Bootstrap confidence sets from the piggyback, and weighted bootstraps are compared for biased sampling data from simulated vaccine efficacy trials.     

半参数变系数部分线性模型的统计推断

本文在多种复杂数据下, 研究一类半参数变系数部分线性模型的统计推断理论和方法. 首先在纵向数据和测量误差数据等复杂数据下, 研究半参数变系数部分线性模型的经验似然推断问题, 分别提出分组的和纠偏的经验似然方法. 该方法可以有效地处理纵向数据的组内相关性给构造经验似然比函数所带来的困难. 其次在测量误差数据和缺失数据等复杂数据下, 研究模型的变量选择问题, 分别提出一个“纠偏” 的和基于借补值的变量选择方法. 该变量选择方法可以同时选择参数分量及非参数分量中的重要变量, 并且变量选择与回归系数的估计同时进行. 通过选择适当的惩罚参数, 证明该变量选择方法可以相合地识别出真实模型, 并且所得的正则估计具有oracle 性质.     

Proportional hazards regression under progressive Type-II censoring

This paper proposes an inferential method for the semiparametric proportional hazards model for progressively Type-II censored data. We establish martingale properties of counting processes based on progressively Type-II censored data that allow to derive the asymptotic behavior of estimators of the regression parameter, the conditional cumulative hazard rate functions, and the conditional reliability functions. A Monte Carlo study and an example are provided to illustrate the behavior of our estimators and to compare progressive Type-II censoring sampling plans with classical Type-II right censoring sampling plan.     

Semiparametric Maximum Likelihood for Missing Covariates in Parametric Regression

We consider parameter estimation in parametric regression models with covariates missing at random. This problem admits a semiparametric maximum likelihood approach which requires no parametric specification of the selection mechanism or the covariate distribution. The semiparametric maximum likelihood estimator (MLE) has been found to be consistent. We show here, for some specific models, that the semiparametric MLE converges weakly to a zero-mean Gaussian process in a suitable space. The regression parameter estimate, in particular, achieves the semiparametric information bound, which can be consistently estimated by perturbing the profile log-likelihood. Furthermore, the profile likelihood ratio statistic is asymptotically chi-squared. The techniques used here extend to other models.     

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In this paper, the semiparametric generalized partially linear models (GPLMs) for longitudinal data is studied. We approximate the nonparametric function in the GPLMs by a regression spline, and use quadratic inference functions (QIF) to take the within-cluster correlation into account without involving direct estimation of nuisance parameters in the correlation matrix. We establish the asymptotic normality of the resulting estimators. The finite sample performance of the proposed methods is evaluated through simulation studies and a real data analysis.