Exchangeably weighted bootstraps of empirical estimators of a semi-Markov kernel

A general notion of bootstrapped empirical estimators, of the semi-Markov kernels and of the conditional transition probabilities for semi-Markov processes with countable state space, constructed by exchangeably weighting sample, is introduced. Asymptotic properties of these generalized bootstrapped empirical distributions are obtained by means of the martingale approach.     

左截断右删失数据分位差估计及其渐近性质

我们研究了左截断右删失数据分位差,基于左截断右删失数据乘积限构造了分位差的经验估计,同时克服经验估计的非光滑性,提出了分位数差的核光滑估计.利用经验过程理论推导出这两个估计的渐近偏差和渐近方差,并且在左截断右删失数据下研究了这两个分位差的大样本性质,获得分位差估计的相合性和渐近正态性.同时给出计算模拟以验证光滑分位差估计的表现,在均方损失的意义下模拟结果表明光滑估计比经验估计具有更好的性质.     

附加信息下的局部线性估计

在回归模型中，对一类因变量函数的条件期望方程的附加信息，我们提出了基于极大经验似然方法的局部线性点估计，在一定条件下证明了这些估计的相合性和渐近正态性，而且估计的方差小于通常不带附加信息核估计的方差．模拟结果也显示了估计的优良性．     

General Asymptotic Confidence Bands Based on Kernel-type Function Estimators

We establish uniform and non-uniform asymptotic simultaneous confidence bands for functionals of the distribution based on kernel-type estimators, which include the Nadaraya-Watson kernel estimators of regression functions and the Akaike-Parzen-Rosenblatt kernel density estimators. Our theorems, based upon functional limit laws derived by modern empirical process theory, allow data-driven local bandwidths for these statistics. This revised version was published online in June 2006 with corrections to the Cover Date.     

Adaptive estimation of an ergodic diffusion process based on sampled data

We consider adaptive maximum likelihood type estimation of both drift and diffusion coefficient parameters for an ergodic diffusion process based on discrete observations. Two kinds of adaptive maximum likelihood type estimators are proposed and asymptotic properties of the adaptive estimators, including convergence of moments, are obtained.     

纵向数据非参数混合效应模型的一个局部不变估计

非参数核回归方法近年来已被用于纵向数据的分析(Lin和Carroll,2000)．一个颇具争议性的问题是在非参数核回归中是否需要考虑纵向数据间的相关性．Lin和Carroll (2000)证明了基于独立性(即忽略相关性)的核估计在一类核GEE估计量中是(渐近)最有效的．基于混合效应模型方法作者提出了一个不同的核估计类,它自然而有效地结合了纵向数据的相关结构．估计量达到了与Lin和Carroll的估计量相同的渐近有效性,且在有限样本情形下表现更好．由此方法可以很容易地获得对于总体和个体的非参数曲线估计．所提出的估计量具有较好的统计性质,且实施方便,从而对实际工作者具有较大的吸引力．     

An Algorithmic Approach to Discrete Time Non-homogeneous Backward Semi-Markov Reward Processes with an Application to Disability Insurance

In this paper semi-Markov reward models are presented. Higher moments of the reward process is presented for the first time applied to in time non-homogeneous semi-Markov insurance problems. Also an example is presented based on real disability data. Different algorithmic approaches to solve the problem is described. This work is partly supported by the Knowledge Foundation and Sparbankens Stiftelse Nya. The authors would like to thank the anonymous referee.     

Maximum likelihood estimation for hidden semi-Markov models

In this Note we consider a discrete-time hidden semi-Markov model and we prove that the nonparametric maximum likelihood estimators for the characteristics of such a model have nice asymptotic properties, namely consistency and asymptotic normality. To cite this article: V. Barbu, N. Limnios, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Varying-coefficient model for the occurrence rate function of recurrent events

This article mainly considers the recurrent event process with independent censoring mechanism through a more flexible varying-coefficient model. The smoothing estimators for the varying-coefficient functions are also proposed via maximizing the kernel weight version of the log-partial likelihood function with respect to the coefficients at each time point. For the selection of appropriate bandwidths and the construction of confidence intervals, the consistent empirical smoothing estimators for the covariance functions of the estimators and a bias correction method are considered. As for the baseline effect function of recurrent events in the population, two different smoothing estimation methods are suggested and investigated. In this study, the asymptotic properties of the proposed smoothing estimators are derived. The finite sample properties of our methods are examined through a Monte Carlo simulation. Moreover, the procedures are applied to a recurrent sample of AIDS link to intravenous experiences (ALIVE) cohort study.     

非负费用折扣半马氏决策过程

本文考虑可数状态非负费用的折扣半马氏决策过程.首先在给定半马氏决策核和策略下构造一个连续时间半马氏决策过程,然后用最小非负解方法证明值函数满足最优方程和存在ε-最优平稳策略,并进一步给出最优策略的存在性条件及其一些性质.最后,给出了值迭代算法和一个数值算例.     

Nonparametric Estimation for Semi-Markov Processes Based on its Hazard Rate Functions

The problem of estimating the Markov renewal matrix and the semi-Markov transition matrix based on a history of a finite semi-Markov process censored at time T (fixed) is addressed for the first time. Their asymptotic properties are studied. We begin by the definition of the transition rate of this process and propose a maximum likelihood estimator for the hazard rate functions and then we show that this estimator is uniformly strongly consistent and converges weakly to a normal random variable. We construct a new estimator for an absolute continous semi-Markov kernel and give detailed derivation of uniform strong consistency and weak convergence of this estimator as the censored time tends to infinity. This revised version was published online in June 2006 with corrections to the Cover Date.     

A note on superkernel density estimators

It is well known that so-called superkernel density estimators have better asymptotic properties than conventional kernel estimators (and generally finite-order estimators) in the case when the density to be estimated is very smooth. In this note, we study asymptotic behavior of the mean integrated square error of superkernel density estimators in the case when the density to be estimated is not very smooth. It turns out that in this case, superkernel estimators still have better asymptotics than finite-order estimators.     

Nonparametric density estimation for linear processes with infinite variance

We consider nonparametric estimation of marginal density functions of linear processes by using kernel density estimators. We assume that the innovation processes are i.i.d. and have infinite-variance. We present the asymptotic distributions of the kernel density estimators with the order of bandwidths fixed as h =  cn ^−1/5, where n is the sample size. The asymptotic distributions depend on both the coefficients of linear processes and the tail behavior of the innovations. In some cases, the kernel estimators have the same asymptotic distributions as for i.i.d. observations. In other cases, the normalized kernel density estimators converge in distribution to stable distributions. A simulation study is also carried out to examine small sample properties.     

含附加信息时条件分位数的估计及其渐近性质

本文利用经验似然方法给出了含附加信息时条件分位数的一类新估计,在一定的正则条件下证明了估计的渐近正态性且渐近方差小于或等于通常的条件分位数核估计的渐近方差．     

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.     

Generalized moment estimation of stochastic differential equations

We study the semiparametric estimation of stochastic differential equations employing methods based on moment conditions, comparing the finite sample and robustness properties of generalized method of moments, empirical likelihood and minimum contrast methods using unconditional and conditional formulations of moment conditions. The results obtained indicate that the estimators proposed, particularly, the estimators based on exponential tilting, obtain better results than those of the generalized methods of moments normally used to estimate stochastic differential equations. This conclusion is mainly derived from the robustness properties of this method in the presence of problems of incorrect specification.     

ψ-混合样本下含附加信息时条件分位数估计的渐近性质

本文利用经验似然方法构造了含附加信息时条件分位数的一类估计,并证明了估计的渐近正态性且渐近方差不大于通常核估计的渐近方差.     

Re-formulation of inverse Gaussian,reciprocal inverse Gaussian,and Birnbaum–Saunders kernel estimators

We reveal the boundary bias problem of Birnbaum–Saunders, inverse Gaussian, and reciprocal inverse Gaussian kernel estimators (Jin and Kawczak, 2003, Scaillet, 2004) and re-formulate these estimators to solve the problem. We investigate asymptotic properties of a new class of asymmetric kernel estimators.     

Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors

Summary This paper establishes the uniform closeness of a weighted residual empirical process to its natural estimate in the linear regression setting when the errors are Gaussian, or a function of Gaussian random variables, that are strictly stationary and long range dependent. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with long range dependent errors. The latter result, in turn, yields the asymptotic distribution of the Jaeckel (1972) rank estimators. The paper also studies the least absolute deviation and a class of certain minimum distance estimators of regression parameters and the kernel type density estimators of the marginal error density when the errors are long range dependent.Research of this author was partly supported by the NSF grant: DMS-9102041