变系数模型中的逐元B-Spline估计法

给出了一种用于估计变系数模型中未知函数的逐元B-Spline方法,建立了估计量的局部渐近偏差,方差和渐近正态分布,开发了一种快速选择估计量窗宽的方法,通过Monte Carlo模拟研究了估计量的有限样本性质.     

Statistical Inference for the Location and Scale Parameters of the Skew Normal Distribution

In this paper, we consider the problem of estimating the location and scale parameters of the skew normal distribution introduced by Azzalini. For this distribution, the classic maximum likelihood estimators(MLEs) do not take explicit forms. We approximate the likelihood equations and derive explicit estimators of the parameters. The bias and variance of the estimators are investigated and Monte Carlo simulation studies show that the estimators are as efficient as the classic MLEs. We demonstrate that the probability coverages of the pivotal quantities (for location and scale parameters) based on asymptotic normality are unsatisfactory, especially when the sample size is small. The use of unconditional simulated percentage points of these quantities is suggested. Finally, a numerical example is used to illustrate the proposed inference methods.     

Maximum likelihood estimation in the proportional hazards cure model

The proportional hazards cure model generalizes Cox’s proportional hazards model which allows that a proportion of study subjects may never experience the event of interest. Here nonparametric maximum likelihood approach is proposed to estimating the cumulative hazard and the regression parameters. The asymptotic properties of the resulting estimators are established using the modern empirical process theory. And the estimators for the regression parameters are shown to be semiparametric efficient.     

带相依终止事件的复发事件数据的可加可乘比率模型

本文对带相依终止事件的复发事件数据提出了一个联合建模分析方法,用一个带脆弱变量的可加可乘比率模型来刻画复发事件过程,还用带脆弱变量的Cox风险率模型来刻画终止事件过程,而且这两个过程的相依性由脆弱变量来刻画.我们利用估计方程的方法,对模型参数进行了估计,给出了所得估计的渐近性质.同时,通过数值模拟分析验证了估计的渐近性质.最后,利用该方法分析了弗吉尼亚大学慢性心脏病病人医疗诊费数据.     

A generalization of the growth curve model which allows missing data

This study presents methods for estimating and testing hypotheses about linear functions of the unknown parameters in a generalization of the growth curve model which allows missing data. The estimators proposed are best asymptotically normal (BAN). A testing method for large samples is described which uses a test criterion given in general form by Wald. The asymptotic null distribution of the test statistic is a central chi-square variable. A BAN estimator of a linear vector function of the unknown parameters of the expectation model and consistent estimators of the variance-covariance parameters are required for computation.     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

A general additive-multiplicative rates model for recurrent event data

In this article, we propose a general additive-multiplicative rates model for recurrent event data. The proposed model includes the additive rates and multiplicative rates models as special cases. For the inference on the model parameters, estimating equation approaches are developed, and asymptotic properties of the proposed estimators are established through modern empirical process theory. In addition, an illustration with multiple-infection data from a clinic study on chronic granulomatous disease is pr...     

成组复发事件下的半参数变换模型

本文在成组复发事件下研究了一个一般半参数的边际变换模型,利用估计方程的理论,给出了该模型中未知参数和基本比率函数的估计,同时利用现代经验过程理论证明了所得估计的相合性和渐近正态性.     

缺失数据下线性EV模型的参数估计

给出EV模型下数据具有随机缺失时,模型参数的一种估计方法,并以一个简单模型为例给出了这种新估计的渐近正态性的具体结果.模拟研究表明,即使在有限样本情形,提出的方法在估计效率上也具有一定优势.     

Analyzing the general biased data by additive risk model

This paper proposes a unified semiparametric method for the additive risk model under general biased sampling. By using the estimating equation approach, we propose both estimators of the regression parameters and nonparametric function. An advantage is that our approach is still suitable for the lengthbiased data even without the information of the truncation variable. Meanwhile, large sample properties of the proposed estimators are established, including consistency and asymptotic normality. In addition, the finite sample behavior of the proposed methods and the analysis of three groups of real data are given.     

Semiparametric analysis of longitudinal data with informative observation times

In many longitudinal studies,observation times as well as censoring times may be correlated with longitudinal responses.This paper considers a multiplicative random effects model for the longitudinal response where these correlations may exist and a joint modeling approach is proposed via a shared latent variable.For inference about regression parameters,estimating equation approaches are developed and asymptotic properties of the proposed estimators are established.The finite sample behavior of the methods is examined through simulation studies and an application to a data set from a bladder cancer study is provided for illustration.     

Efficient parameter estimation via modified Cholesky decomposition for quantile regression with longitudinal data

It is well known that specifying a covariance matrix is difficult in the quantile regression with longitudinal data. This paper develops a two step estimation procedure to improve estimation efficiency based on the modified Cholesky decomposition. Specifically, in the first step, we obtain the initial estimators of regression coefficients by ignoring the possible correlations between repeated measures. Then, we apply the modified Cholesky decomposition to construct the covariance models and obtain the estimator of within-subject covariance matrix. In the second step, we construct unbiased estimating functions to obtain more efficient estimators of regression coefficients. However, the proposed estimating functions are discrete and non-convex. We utilize the induced smoothing method to achieve the fast and accurate estimates of parameters and their asymptotic covariance. Under some regularity conditions, we establish the asymptotically normal distributions for the resulting estimators. Simulation studies and the longitudinal progesterone data analysis show that the proposed approach yields highly efficient estimators.     

Estimation of parameters in the discrete distributions of order k

This paper considers estimating parameters in the discrete distributions of order k such as the binomial, the geometric, the Poisson and the logarithmic series distributions of order k. It is discussed how to calculate maximum likelihood estimates of parameters of the distributions based on independent observations. Further, asymptotic properties of estimators by the method of moments are investigated. In some cases, it is found that the values of asymptotic efficiency of the moment estimators are surprisingly close to one.     

纵向数据混合效应模型的统计分析

本文研究了Tao等人在1999年提出的半参数混合效应模型,在不假设随机效应服从正态分布的条件下,用傅立叶变换的方法构造了随机效应的光滑非参数密度估计,给出了密度估计的公式,研究了其渐近性质,还构造了半参数混合效应模型中参数的估计方法并研究了其大样本性质。     

A class of additive-accelerated means regression models for recurrent event data

In this article, we propose a class of additive-accelerated means regression models for analyzing recurrent event data. The class includes the proportional means model, the additive rates model, the accelerated failure time model, the accelerated rates model and the additive-accelerated rate model as special cases. The new model offers great flexibility in formulating the effects of covariates on the mean functions of counting processes while leaving the stochastic structure completely unspecified. For the inference on the model parameters, estimating equation approaches are derived and asymptotic properties of the proposed estimators are established. In addition, a technique is provided for model checking. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is illustrated.     

Asymptotics on Semiparametric Analysis of Multivariate Failure Time Data Under the Additive Hazards Model

Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time data under the additive hazards model. Simple weighted estimating functions for the regression parameters are proposed, and asymptotic distribution theory of the resulting estimators are derived. In addition, a class of generalized Wald and generalized score statistics for hypothesis testing and model selection are presented, and the asymptotic properties of these statistics are examined.     

加速方程有偏场合下加速寿命试验的稳健设计

考虑在加速寿命试验中,当假定的加速模型不是转化应力的线性模型时,模型参数的极大似然估计的近似分布。研究在一定的条件下,获得正常应力下寿命分布的p分位寿命估计的最优稳健设计方法。并通过数值例子说明方法的有效性。     

Robust Estimation in Partial Linear Mixed Model for Longitudinal Data

In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.     

Asymptotically optimal estimation in the linear regression problem in the case of violation of some classical assumptions

We consider the problem of estimating the unknown parameters of linear regression in the case when the variances of observations depend on the unknown parameters of the model. A two-step method is suggested for constructing asymptotically linear estimators. Some general sufficient conditions for the asymptotic normality of the estimators are found, and an explicit form is established of the best asymptotically linear estimators. The behavior of the estimators is studied in detail in the case when the parameter of the regression model is one-dimensional.     

Non-parametric kernel regression for multinomial data

This paper presents a kernel smoothing method for multinomial regression. A class of estimators of the regression functions is constructed by minimizing a localized power-divergence measure. These estimators include the bandwidth and a single parameter originating in the power-divergence measure as smoothing parameters. An asymptotic theory for the estimators is developed and the bias-adjusted estimators are obtained. A data-based algorithm for selecting the smoothing parameters is also proposed. Simulation results reveal that the proposed algorithm works efficiently.