一般生长曲线模型的GME及其稳健性

本文考虑协差阵V_2(?)V_1≥0时,生长曲线模型中未知参数阵B的线性可估函数KBL的估计问题,给出了KBL的形如V_2(?)V_1>0时的GME,讨论了GM性与SD性的关系,给出了设计阵、散布阵发生偏离时保持GME不变的条件。     

分片逆回归中的渐近推断

分片逆回归是最近提出的一种多元数据分析方法.这是一种有效的降维方法.使用该方法的关键点在于能给出条件协差阵一个较好的估计.为此目的,本文基于拟残差给出了一个估计,并且研究了它的渐近性质,最后给出了部分模拟结果.     

诊断复共线性的新方法

本文提出诊断线性模型复共线性的新观点和规则,给出诊断复共线性的新方法和算法以及当复共线性存在时自变量的近似线性表示。用例子生动地说明了本文方法的合理性、可行性和运算过程的简单性。     

具有二次函数型协差阵的多参数指数族

对以均值为参数的多参数指数族,本文指出,协差阵元素为均值的k阶多项式时,其Bh-阵具有简单形式:它的子块B(i,j)=0,对j>(k-1)(i-1)+1,i=1,2,…,于是对k≥2(二次函数型协差阵)情形,Bh-阵的非对角子块均为零阵。本文给出了其对角子块的递推表达式,最后我们讨论了k≤2情形的多参数指数族形式。可看出它们基本是单参数指数族k≤2情形的自然推广。     

多周期Probit模型中MLE的存在性

本文我们讨论了多周期Probit模型中MLE的存在性问题,给出了当协方差阵已知时,参数的MLE存在的充要条件;当协方差阵未知但具有序列结构时,参数的MLE存在的一个必要条件和一个充分条件.     

多元线性模型参数的部分压缩估计

考虑多元线性回归模型Y=XB ε,其中E(Vec(ε))=0,Cov(Vec(ε))=∑In,当设计阵X呈病态时,模型参数的LS估计不再是一个优良估计,为此,提出了一种部分压缩估计,并分析了其性质.     

生长曲线模型中协差阵的最优非负估计

本文给出了一个判定非负定阵的新方法,完成了生长曲线模型中误差协差阵非负估计理论的下列工作:(1)最优估计存在的充要条件及存在时的显示表达;(2)任意二次估计为最优估计的充要条件,作为推论给出了最小二乘估计为最优非负估计的充要条件;(3)给出了一个优于最小二乘估计的新估计.     

不完全资料下logistic回归模型参数估计的EM算法

本文讨论了带有不完全观测协变量的资料的logistic,回归模型。在假设不完全是由于部分观测个体随机缺失(missing at random.MAR)部分协变量的前提下,给出了参数的极大似然估计的EM算法,并导出观测信息阵的具体形式。最后以实例加以验证。     

广义多元分布参数检验的无偏性

在许多实际问题中,我们通常预先对母体均值和协差阵的结构作了假定.如:对一个母体我们假设:μ=0,∑=I;或μ=0,Σ=σ~2I.对多个母体我们假设所有母体的均值和协差阵相等等等.对这些假设我们都应进行检验,看我们的假设是否成立,所以我们就得研究母体的均值、协差阵的假设检验问题.我们知道对于多元正态母体、均值、协差阵检验的似然比检验具有许多良好的性质,比如具有无偏性等等.在这篇文章中,我们将证明这些检验在第三类椭球等高分布族里仍然具备无偏性.     

关于分数稳定过程分数参数的注

注意到分数稳定过程的样本性质和分布特征都密切关联于其分数参数,本文进一步刻画分数稳定过程关于分数参数的正则性及其对过程协差的影响.     

Improved estimation under collinearity and squared error loss

This paper examines the performance of several biased, Stein-like and empirical Bayes estimators for the general linear statistical model under conditions of collinearity. A new criterion for deleting principal components, based on an unbiased estimator of risk, is introduced. Using a squared error measure and Monte Carlo sampling experiments, the resulting estimator's performance is evaluated and compared with other traditional and non-traditional estimators.     

Adaptive Unified Biased Estimators of Parameters in Linear Model

To tackle multi collinearity or ill-conditioned design matrices in linear models,adaptive biasedestimators such as the time-honored Stein estimator,the ridge and the principal component estimators havebeen studied intensively.To study when a biased estimator uniformly outperforms the least squares estimator,some sufficient conditions are proposed in the literature.In this paper,we propose a unified framework toformulate a class of adaptive biased estimators.This class includes all existing biased estimators and some newones.A sufficient condition for outperforming the least squares estimator is proposed.In terms of selectingparameters in the condition,we can obtain all double-type conditions in the literature.     

Kernel quantile estimator with ICI adaptive bandwidth selection technique

In this article, we consider a class of kernel quantile estimators which is the linear combi- nation of order statistics. This class of kernel quantile estimators can be regarded as an extension of some existing estimators. The exact mean square error expression for this class of estimators will be provided when data are uniformly distributed. The implementation of these estimators depends mostly on the bandwidth selection. We then develop an adaptive method for bandwidth selection based on the intersection confidence intervals （ICI） principle. Monte Carlo studies demonstrate that our proposed approach is comparatively remarkable. We illustrate our method with a real data set.     

On the dispersion matrix of variance estimators of the sample mean in the analysis of simulation output

A classical problem of stochastic simulation is how to estimate the variance of point estimators, the prototype problem being the sample mean from a steady-state autocorrelated process. A variety of estimators for the variance of the sample mean have been proposed, all designed to provide robustness to violations of assumptions, small variance, and reasonable computing requirements. Evaluation and comparison of such estimators depend on the ability to calculate their variances.A numerical approach is developed here to calculate the dispersion matrix of a set of estimators expressible as quadratic forms of the data. The approach separates the analysis of the estimator type from the analysis of the data type. The analysis for overlapping-batch-means estimators is developed, as is the analysis for steady-state first-order autoregressive and moving-average data. Closed-form expressions for overlapping-batch-means estimators and independently distributed data are obtained.     

Inference for a simple step-stress model based on ordered ranked set sampling

In this paper, we considered the inference problem on simple step-stress accelerated life test data from one-parameter exponential distribution under type-I censored ordered ranked set sample with cumulative exposure model. The Bayesian estimators and credible intervals for the model parameters are developed and compared with the corresponding estimators based on simple random sampling. Two real data sets and numerical simulation evaluations are presented to illustrate all the results developed here. The simulation study indicated that the proposed Bayes estimators and credible intervals based on ordered ranked set sampling performed better than their counterparts using simple random sampling.     

An efficient risk estimator with external information under additive hazards model

Rare event data is encountered when the events of interest occur with low frequency, and the estimators based on the cohort data only may be inefficient. However, when external information is available for the estimation, the estimators utilizing external information can be more efficient. In this paper, we propose a method to incorporate external information into the estimation of the baseline hazard function and improve efficiency for estimating the absolute risk under the additive hazards model. The resulting estimators are shown to be uniformly consistent and converge weakly to Gaussian processes. Simulation studies demonstrate that the proposed method is much more efficient. An application to a bone marrow transplant data set is provided.     

Perturbation analysis for circles, spheres, and generalized hyperspheres fitted to data by geometric total least-squares

A continuous extension of the objective function to a projective space guarantees that for each data set there exists at least one hyperplane or hypersphere minimizing the average squared distance to the data. For data sufficiently close to a hypersphere, as the collinearity of the data increases, so does the sensitivity of the fitted hypersphere to perturbations of the data.

     

A general framework for frequentist model averaging In Celebration of Professor Lincheng Zhao's 75th Birthday

Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. Model averaging approaches, on the other hand, try to combine estimators for a set of candidate models. Specifically, instead of deciding which model is the 'right' one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using data adaptive weights.In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It broaden, the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account.We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.     

Assessing the performance of empirical bayes estimators

Methods for deriving empirical Bayes estimators are generally available. Corresponding general techniques for assessing the performance of these estimators are not widely developed yet, however. In this paper we provide a general procedure for assessing and comparing the performance of the empirical Bayes estimators and other estimators in a given data set.     

Robust Frequency Estimation Using Elemental Sets

Abstract

The extraction of sinusoidal signals from time-series data is a classic problem of ongoing interest in the statistics and signal processing literatures. Obtaining least squares estimates is difficult because the sum of squares has local minima O(1/n) apart in the frequencies. In practice the frequencies are often estimated using ad hoc and inefficient methods. Problems of data quality have received little attention. An elemental set is a subset of the data containing the minimum number of points such that the unknown parameters in the model can be identified. This article shows that, using a variant of the classical method of Prony, parameter estimates for a sum of sinusoids can be obtained algebraically from an elemental set. Elemental set methods are used to construct finite algorithm estimators that approximately minimize the least squares, least trimmed sum of squares, or least median of squares criteria. The elemental set estimators prove able in simulations to resolve the frequencies to the correct local minima of the objective functions. When used as the first stage of an MM estimator, the constructed estimators based on the trimmed sum of squares and least median of squares criteria produce final estimators which have high breakdown properties and which are simultaneously efficient when no outliers are present. The approach can also be applied to sums of exponentials, and sums of damped sinusoids. The article includes simulations with one and two sinusoids and two data examples.