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.     

Improvement in estimating the population mean in simple random sampling using information on auxiliary attribute

This paper proposes some estimators for the population mean by adapting the estimator in Singh et al. (2008) [5] to the ratio estimators presented in Kadilar and Cingi 2006 [2]. We obtain mean square error (MSE) equation for all proposed estimators, and show that all proposed estimators are always more efficient than ratio estimator in Naik and Gupta (1996) [3], and Singh et al. (2008) [5]. The results have been illustrated numerically by taking some empirical population considered in the literature.     

多个子样本下过程能力指数估计量的比较研究

过程能力指数(C_p)估计的关键是对总体标准差的估计。在多个子样本情形下,采用4个无偏估计量■,■_s,■_R,■_p分别估计总体标准差σ,证明了直接以此为基础的过程能力指数的估计量都是有偏的,且都有高估C_p的倾向;之后构造了C_p的4个无偏估计量;探讨了其中3个无偏估计量的估计效率;最后结合案例计算了C_p的不同估计值。     

随机截断模型下生存函数的一个估计

本文讨论截断数据生存函数的估计问题。由于在寿命试验中截断分布Ｇ（ｙ）往往是人们５自己设计的，从类似Ｂｕｃｋｌｅｙ和Ｊａｍｅｓ处理期望的思想出发，文中给出了一个新的估计，并计算了它的期望和方差。     

删失数据下回归函数的最近邻估计

设（X，Y）是一随机向量且变量Y的均值存在．假定Y被另一分布G的随机变量t删失，仅能观察到不完全数据（xi，Yi^ti,δi），i＝1，2，…n，其中Yi^ti＝min（Yi，Ti）,δi=I（Yi≤ti）。为了给出回归函数m（x）＝E（Y|X）的估计。文中使用了Stute提出的最近邻型回归估计，并给出了该估计的强相合性结果．     

A POSTERIORI ESTIMATOR OF NONCONFORMING FINITE ELEMENT METHOD FOR FOURTH ORDER ELLIPTIC PERTURBATION PROBLEMS

In this paper, we consider the nonconforming finite element approximations of fourth order elliptic perturbation problems in two dimensions. We present an a posteriori error estimator under certain conditions, and give an h-version adaptive algorithm based on the error estimation. The local behavior of the estimator is analyzed as well. This estimator works for several nonconforming methods, such as the modified Morley method and the modified Zienkiewicz method, and under some assumptions, it is an optimal one. Numerical examples are reported, with a linear stationary Cahn-HiUiard-type equation as a model problem.     

一个矩阵不等式和Bayes无偏估计（英）

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MARS: selecting basis functions and knots with an empirical Bayes method

An empirical Bayes method to select basis functions and knots in multivariate adaptive regression spline (MARS) is proposed, which takes both advantages of frequentist model selection approaches and Bayesian approaches. A penalized likelihood is maximized to estimate regression coefficients for selected basis functions, and an approximated marginal likelihood is maximized to select knots and variables involved in basis functions. Moreover, the Akaike Bayes information criterion (ABIC) is used to determine the number of basis functions. It is shown that the proposed method gives estimation of regression structure that is relatively parsimonious and more stable for some example data sets.     

Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs

For partial linear model Y=X~τβ_0 _(g0)(T) εwith unknown β_0∈R~d and an unknown smooth function go, this paper considers the Huber-Dutter estimators of β_0, scale σfor the errors and the function go respectively, in which the smoothing B-spline function is used. Under some regular conditions, it is shown that the Huber-Dutter estimators of β_0 and σare asymptotically normal with convergence rate n~((-1)/2) and the B-spline Huber-Dutter estimator of go achieves the optimal convergence rate in nonparametric regression. A simulation study demonstrates that the Huber-Dutter estimator of β_0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. An example is presented after the simulation study.