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.     

半参数混合效应模型中的估计及其强相合性

将Tao等(1999)提出的线性混合效应模型推广为半参数混合效应模型,给出了模型参数、回归函数和随机效应密度的估计,并研究了估计的强相合性及部分强相合速度.统计模拟表明我们给出的估计方法是可行的.     

相协样本半参数回归模型估计的矩相合性

考虑半参数回归模型Y(j) (xin,tin) =tinβ g(xin) e(j) (xin) ,1 ≤j≤m ,1 ≤i≤n .利用最小二乘法和权函数估计方法 ,定义 β ,g的估计量βm ,n和gm ,n(x) ,在负相依样本及较弱的条件下证明了这些估计的矩相合性 ,这些结论推广和改进了胡舒合 ( 1 997)关于独立情形的相应结论 .     

半参数回归模型的两步估计——差分法和样条函数法

本文考虑半参数回归模型yi =XTiβ g(ti) ei(i =1 ,2 ,… ,n) .先利用差分的方法估计 ^β ,接着用样条函数的方法定义 ^g(T) ,最后讨论 ^g(t)的性质 .     

多维GARCH模型的半参数有效估计

多元GARCH模型的估计一般采用拟极大似然法(quasi maximum likehood),对于这种方法估计的相合性及渐近正态性已经被很多学者证实,然而对于新息列的分布不是多元正态时,这种估计的有效性还没人研究,本文从拟极大似然估计得到的参数相合估计入手,提出用非参数方法估计多元新息列的分布.     

Estimating household purchase rates for consumer nondurable goods

Understanding the purchase rates of households for frequently purchased packaged goods is an important element in developing effective marketing strategies. Previous researchers have attempted to estimate these rates by assuming that the time between purchases is a random variable that follows some common parametric probability distribution such as the exponential or Weibull distribution. Recent research has shown that for many frequently purchased packaged goods, the interpurchase times cannot be adequately described by these commonly used probability distributions. In this study we demonstrate how household purchase rates can be estimated in a robust manner using a generalized semiparametric approach that obviates the need for specifying a parametric form for the distribution of interpurchase times. The motivation being that often there is no theory of household purchase behaviour that specifies a priori the probability distribution underlying the interpurchase times. Our empirical results indicate that, for the data analysed, the household purchase rates exhibit a regular pattern that cannot be recovered by probability distributions often used in previous research. Further, marketing actions taken by sellers do indeed influence household purchase behaviour.     

BAHADUR ASYMPTOTIC EFFICIENCY IN A SEMIPARAMETRIC REGRESSION MODEL

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Preservation of transform orders under a semiparametric model and its mixture

In this paper, sufficient conditions for preservation of several transform orders under a typical family of semiparametric distributions are made. The preservation properties are developed to compare mixture semiparametric distributions. Possible applications of the achieved results to compare scale family of distributions and also compare coherent systems with dependent but identical components and series and parallel systems with randomized number of components are provided.     

Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated based on the effective score, which is obtained by determining the component of the parametric score orthogonal to the space generated by the infinite-dimensional nuisance parameter. The asymptotic distributions of the maximum pseudolikelihood and related estimators in an i.i.d. setting show that these estimators do not achieve the computed asymptotic lower bound. Simple guidelines are provided to determine in which instances such estimators are close enough to efficient for practical purposes.     

半参数回归模型中小波估计的随机加权逼近速度

把小波光滑方法和随机加权方法结合在一起，获得了半参数回归模型中参数分量的小波估计的随机加权逼近速度为σ(n^-1/2)。因此，从大样本意义上说，小波光滑方法和随机加权方法对半参数回归模型是可用的。