指数族下参数双边检验的p-值

在单参数指数族下,对参数的双侧检验问题给出了一致最优检验或一致最优无偏检验的p-值;在多参数指数族下,对单个参数双侧检验问题给出了一致最优无偏检验的p-值.在正态总体下,给出了几个计算上述p-值的例子.     

固定设计下非参数回归模型估计的渐近性质

考虑固定设计下具有非参数AR(1)的非参数回归模型,综合最小二乘和非参数核估计法,定义了非参数函数的估计量,在适当的条件下,研究了它们的渐近性质.     

不确定参数下群体博弈均衡的存在性与通有稳定性

本文在已知不确定参数变化范围的假设下,研究了不确定参数下群体博弈均衡的存在性与通有稳定性.首先,基于经典非合作博弈NS均衡概念提出了不确定参数下群体博弈NS均衡的定义;其次,在支付函数连续性与凸性的一定假设下,利用Ky Fan不等式证明了均衡的存在性;最后,给出了不确定参数下群体博弈模型NS均衡集通有稳定性的相关结论,运用Fort引理证明了在Baire分类的意义下,当支付函数发生扰动时,大多数不确定参数下群体博弈的NS均衡点集都是稳定的.     

一类线性回归模型中核估计的渐近性质

考虑固定设计下具有一阶非参数自回归误差的线性模型,构造了参数和非参数函数的N-W核估计,在适当的条件下,证明了参数估计的强相合性,同时给出了非参数函数估计的渐近正态性.     

纵向数据下半参数回归模型的统计分析

对于纵向数据下半参数回归模型,基于广义估计方程和一般权函数方法构造了模型中参数分量和非参数分量的估计.在适当的条件下证明了参数估计量具有渐近正态性,并得到了非参数回归函数估计量的最优收敛速度.通过模拟研究说明了所提出的估计量在有限样本下的精确性.     

Weibull分布步进应力加速寿命试验的Bayes估计

本文研究了定时和定数截尾情形CE模型下Weibull分布场合步进应力加速寿命试验的Bayes估计.利用加速系数和加速方程将各种加速应力水平下的尺度参数换算为正常应力水平下的尺度参数,从而获得含正常应力下尺度参数的似然函数.在参数先验的选取时,尺度参数和加速系数分别取共轭先验和无信息先验,当形状参数m<1和m>1时分别取Beta分布和Gamma分布作为其先验.在平方损失下,利用Gibbs抽样和切片抽样给出了该模型参数的Bayes估计.最后,通过Monte Carlo模拟表明该Bayes估计是有效的.     

一类过程摄动系统的无阻塞鲁棒性

使用参数Dioid模块网络法,把含大量摄动参数的在普通极大代数意义下非线性状态空间模型在参数Dioid意义下线性化,在此基础上研究一类过程摄动系统的无阻塞鲁棒性.给出了有限缓冲串行生产系统在没有缓冲器下无阻塞的充要条件和充分条件.     

熵损失函数下两参数指数威布尔分布尺度参数的Bayes估计

本文给定一截尾样本，在熵损失函数下，研究了两参数指数威布尔分布尺度参数在先验伽玛分布下的Bayes估计，并给出了该参数的Bayes区间估计。     

定数截尾两参数指数——威布尔分布形状参数的Bayes估计

在不同的损失函数下,本文研究了两参数指数—威布尔分布(EWD)形状参数的Bayes估计问题.基于定数截尾试验,当其中一个形状参数α已知时,给出了另一个形状参数θ在三种不同损失函数下的Bayes估计表达式,并求得了可靠度函数的Bayes点估计.最后运用随机模拟方法,将Bayes估计和极大似然估计进行了比较.结果表明,LINEX损失下Bayes估计的精度比极大似然估计高.     

NA样本下随机设计的半参数回归模型的弱相合性

本文研究了误差为NA序列下随机设计的半参数回归模型的问题.利用权函数和最小二乘估计的方法给出了参数、非参数及误差方差的估计,在较弱的条件下获得了它们的弱相合性结果.     

On near neighbour estimates of a multivariate density

A recent paper by Mack and Rosenblatt (J. Multivar. Anal.9 (1979), 1–15) has shown that near neighbour estimators of a density may perform more poorly than other kernel-type estimators, particularly for x values in the tail of a distribution. In order to overcome the difficulties discovered by Mack and Rosenblatt, a generalized type of near neighbour estimator is proposed. Here the window size, or bandwidth, is chosen as a function of near neighbour distances, rather than actually equal to one of the distances. Two forms for this function are suggested and it is proved that for large samples the resulting estimator does not suffer the drawbacks of the usual near neighbour estimator.     

鞅差误差序列下半参数EV回归模型的近邻估计

本文研究了误差为鞅差序列的条件下的一维半参数EV回归模型.利用两步估计的方法构造了参数分量和非参数分量的近邻估计,并且分别证明了估计量的L2相合性和强相合性,从而推广了在普通半参数回归模型已有的相关结论.     

Pointwise Improvement of Multivariate Kernel Density Estimates

Multivariate kernel density estimators are known to systematically deviate from the true value near critical points of the density surface. To overcome this difficulty a method based on Rao–Blackwell's theorem is proposed. Local corrections of kernel density estimators are achieved by conditioning these estimators with respect to locally sufficient statistics. The asymptotic as well as the small sample size behavior of the improved estimators are studied. Asymptotic bias and variance are investigated and weak and complete consistency are derived under mild hypothesis.     

Adaptation under probabilistic error for estimating linear functionals

The problem of estimating linear functionals based on Gaussian observations is considered. Probabilistic error is used as a measure of accuracy and attention is focused on the construction of adaptive estimators which are simultaneously near optimal under probabilistic error over a collection of convex parameter spaces. In contrast to mean squared error it is shown that fully rate optimal adaptive estimators can be constructed for probabilistic error. A general construction of such estimators is provided and examples are given to illustrate the general theory.     

Minimax multivariate empirical Bayes estimators under multicollinearity

In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage functions, that is, scalar, componentwise and matricial shrinkage. These proposed estimators are proved to be uniformly better than the least squares estimator, that is, minimax in terms of risk under the Strawderman's loss function. Through simulation and empirical studies, they are also shown to be useful in the multicollinearity cases.     

Detection of the jump points of a heteroscedastic regression model by wavelets

1. IntroductionDetection of jump points often arises in many practical problems such as signal analysis,.... fimage processing, seismic exploratioll and phonetic identification. FOr examPle, financialeconollilsts often wad to know if abrupt changes occur in an exchange rate series sincethese changes edicted, are affecting or will affect fin-ancial market; engineers concern abolltwhether there exist jumps in a seismic signal in oil exploration bacause these jumps maypredict that there exists br…     

The Hill estimators under power normalization

By using the link between the affine and the power norming, eight Hill estimators under power normalization for the tail index (the non-zero extreme value index) are suggested. Moreover, more compact and adaptive four Hill estimators under power normalization are derived based on the generalized Pareto distributions under power normalization. Two classes of harmonic t-Hill estimators under power normalization are also suggested. A comprehensive simulation study using the R-package shows that all the suggested estimators under power normalization work well, but in all cases the Hill estimators under power normalization based on Pareto distributions under power normalization are better. The two models under linear and power normalization for extreme value analysis are applied with comparison on a real data set of two pollutants, Sulphur Dioxide and Particulate Matter.     

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling(RSS) called moving extremes RSS(MERSS) is considered for the estimation of the scale and shape parameters for the log-logistic distribution. Several traditional estimators and ad hoc estimators will be studied under MERSS. The estimators under MERSS are compared to the corresponding ones under SRS. The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.     

Minimax estimator of regression coefficient in normal distribution under balanced loss function

This article investigates linear minimax estimators of regression coefficient in a linear model with an assumption that the underlying distribution is a normal one with a nonnegative definite covariance matrix under a balanced loss function. Some linear minimax estimators of regression coefficient in the class of all estimators are obtained. The result shows that the linear minimax estimators are unique under some conditions.     

Sample rotation theory with missing data

This paper studies how the sample rotation method is applied to the case where item non-response occurs in surveys. The two cases where the response to the first occasion is complete or incomplete are considered. Using ratio imputation method, the estimators of the current population mean are proposed, which are valid under uniform response regardless of the model and under the ratio model regardless of the response mechanism. Under uniform response, the variances of the proposed estimators are derived. Interestingly, although their expressions are similar, the estimator for the case of incomplete response on the first occasion can have smaller variance than the one for the case of complete response on the first occasion under uniform response. The linearized jackknife variance estimators are also given. These variance estimators prove to be approximately design-unbiased under uniform response. It should be noted that similar property on variance estimators has not been discussed in literature.