Minimum divergence estimators,maximum likelihood and exponential families

The dual representation formula of the divergence between two distributions in a parametric model is presented. Resulting estimators do not make use of any grouping or smoothing. For smooth divergences they all coincide with the MLE on any regular exponential family.     

平衡指数损失函数下的信度保费

在经典的信度保费模型中,得到的信度保费估计均是考虑的是纯保费,然而在保险实务中,保险公司收取的保费不可能是纯保费,必须具有正的安全负荷.在平衡指数损失函数下,研究了多合同的信度保费模型.利用正交投影方法,得到了未来保费的信度估计.最后对估计进行了数值模拟.     

Quasi-maximum likelihood estimators in generalized linear models with autoregressive processes

The paper studies a generalized linear model(GLM)y_t = h(x_t~T β) + ε_t,t = l,2,...,n,where ε_1 = η_1,ε_1 =ρε_t +η_t,t = 2,3,...;n,h is a continuous differentiable function,η_t's are independent and identically distributed random errors with zero mean and finite variance σ~2.Firstly,the quasi-maximum likelihood(QML) estimators of β,p and σ~2 are given.Secondly,under mild conditions,the asymptotic properties(including the existence,weak consistency and asymptotic distribution) of the QML estimators are investigated.Lastly,the validity of method is illuminated by a simulation example.     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.     

部分线性模型的随机约束岭估计

研究了部分线性回归模型附加有随机约束条件时的估计问题.基于Profile最小二乘方法和混合估计方法提出了参数分量随机约束下的Profile混合估计,并研究了其性质.为了克服共线性问题,构造了参数分量的Profile混合岭估计,并给出了估计量的偏和方差.     

相依样本时条件密度双重核估计 的渐近正态性’

本文证 明了孙东初在 〕 中提 出的条件密度双重核 估计。川 幻 在样 本为甲一混 合时的渐近正态性     

线性模型参数M估计的强相合性

本文研究线性模型中回归参数　Ｍ　估计的强相合性，　给出一些较弱的充分条件．　与陈希孺和赵林城的专著［１］中相应的结论比较，　这里给出的条件对矩的要求有较大的实质性改进．     

Hypotheses Testing for Error-in-Variables Models

In this paper, hypotheses testing based on a corrected score function are considered. Five different testing statistics are proposed and their asymptotic distributions are investigated. It is shown that the statistics are asymptotically distributed according to the chisquare distribution or can be written as a linear combination of chisquare random variables with one degree of freedom. A small scale numerical Monte Carlo study is presented in order to compare the empirical size and power of the proposed tests. A comparative calibration example is used to illustrate the results obtained.     

Strong limit theorems for oscillation moduli of PL-process and cumulative hazard process under truncation and censorship with applications

In this paper we obtain exact rates of uniform convergence for oscillation moduli and Lipschitz-1/2 moduli of PL-process and cumulative hazard process when the data are subject to left truncation and right censorship. Based on these results, the exact rates of uniform convergence for various types of density and hazard function estimators are derived. Research supported by the Postdoctoral Programme Foundation and the National Natural Science Foundation of China     

Frontier estimation with local polynomials and high power-transformed data

We present a new method for estimating the frontier of a sample. The estimator is based on a local polynomial regression on the power-transformed data. We assume that the exponent of the transformation goes to infinity while the bandwidth goes to zero. We give conditions on these two parameters for obtaining almost complete convergence. The asymptotic conditional bias and variance of the estimator are provided and its good performance is illustrated for some finite sample situations.