部分变量带误差的线性函数关系模型的参数估计及相合性

本文讨论了部分变量带误差的线性函数关系模型的参数估计问题，在较弱条件下证明了所获得的估计的强相合性，并给出了收敛速度。     

部分线性模型中参数分量与非参数分量估计的收敛速度

对于部分线性回归模型,基于未知函数 ｆ （·） 与 ｇ （·） 分别取一类核估计和最近邻估计,文中构造了参数β的最小二乘估计β和加权最小二乘估计β,获得了参数β估计量的渐近正态性与函数ｇ （·） 估计量的最优弱收敛速度。     

股价分析与网点观测函数关系模型

文中提出了一种可用于股价分析的网点观测函数关系模型，得到了模型参数的估计，在一定条件下，证明了估计量是强相合估计，并得出了收敛速度，计算地股市实际有一定的参考价值。     

纵向数据半参数回归模型估计的强相合性

本文考虑如下纵向数据半参数回归模型:yij=x'ijβ g(tij) eij。基于最小二乘法和一般的非参数权函数方法给出了模型中参数β,回归函数g(·)和误差方差σ2的估计,并在适当条件下证明了估计量的强相合性。     

线性过程方差变点的估计

本文研究线性过程方差变点的估计问题,给出了变点的CUSUM型估计量.在误差不相依情形下得到了线性过程的Hájek-Rényi型不等式,在较弱的条件下推导出了估计量的收敛速度,最后模拟结果证实本文的结论.     

具有非参数AR(1)误差的回归模型的局部线性估计

考虑随机设计下具有一阶非参数自回归误差的线性回归模型,构造了参数和非参数函数的局部线性估计。在适当的条件下,证明了参数估计量的渐近正态性,并给出了非参数函数估计的收敛速度。模拟算例表明局部线性方法优于核方法。     

误差方差不等的变量含误差直线回归模型──参数的驻点似然估计及强相合性

本文讨论了含有一个自变量且自变量误差方差与因变量误差方差不等的变量合误差线性回归模型。由于对这种模型最大似然估计失去作用，文中提出了一种新的估计方法──驻点似然估计。这种方法就是，用使似然函数达到驻点的参数值作为参数真值的估计。作为此估计法的实际应用，本文导出了所讨论模型的参数的驻点似然估计。然后证明了所得到的估计在一定条件下是模型参数的强相合估计。     

误差为线性过程时非参数回归模型变点的两步估计

本文给出误差为线性过程时非参数回归模型变点两步估计.第一步,给出变点位置的初始估计,并且证明了该估计量的相合性;第二步,在变点初始估计值的基础上推导出变点位置的最终估计量并给出了该估计量的收敛速度.数值模拟以及尼罗河数据实例分析的结果说明方法的有效性.     

部分变量含误差的多重线性统计关系模型

本文讨论了一部分变量含误差的多重线性统计关系模型的参数估计问题。在观测误差是正态白噪声的条件下,我们导出了模型参数的最大似然估计。为了解决相合性研究中参数的不确定性问题,在文中引进了准强相合性的概念,并证明了所给出的参数估计量具有准强相合性。     

遗漏变量下多元非参数核估计渐近偏误的一致估计框架

在经济学、社会学、医学、生物学、农业等诸领域的研究中，由于数据获取的困难、实验条件的限制、研究经验的不足以及失误等因素，研究者往往会在回归模型的设定中遗漏掉关键的解释变量，使得遗漏变量模型的识别与处理成为一个广泛存在的问题。由此，提出了一种统一的识别、估计与比较框架，使得针对遗漏变量回归模型的任意非参数核估计量的渐近偏误都可以得到识别与估计。应用此框架，考察了遗漏变量下Nadaraya-Watson估计量、Gasser-M¨uller估计量以及局部线性估计量的精确渐近性质，发现遗漏变量下Gasser-M¨uller估计量与局部线性估计量的渐近偏误一样大，且都比Nadaraya-Watson估计量的渐近偏误小。此外遗漏变量下线性参数模型估计量的渐近性质也可以通过本文提出的框架与方法推导出来。在此基础上，进一步探讨了局部线性核估计量的一个没被注意到的优良性质。     

Proceedings of the Computer Science and Statistics: 12th Annual Symposium on the Interface

This article examines the properties of smoothed estimators of the probabilities of misclassification in linear discriminant analysis and compares them with those of the resubstitution, leave-one-out, and bootstrap estimators. Smoothed estimators are found to have smaller variance than the other estimators and bias that is a function of the amount of smoothing. An algorithm is presented for determining a reasonable level of smoothing as a function of the training sample sizes and the number of dimensions in the observation vector. Using the criterion of unconditional mean squared error, this particular smoothed estimator, called the NS method, appears to offer a reasonable alternative to existing nonparametric estimators.     

Recursive local polynomial regression under dependence conditions

In the case of the random design nonparametric regression, one recursive local polynomial smoother is considered. Expressions for the bias and the variance matrix of the estimators of the regression function and its derivatives are obtained under dependence conditions (strongly mixing processes). The obtained Mean Squared Error is shown to be larger than those of the analogous nonrecursive regression estimators, although retaining the same convergence rate. The properties of strong consistency with convergence rates are established for the proposed estimators. Finally, in order to analyse the influence of both the sample size and the dependence in the behaviour of the proposed recursive estimator, a simulation study is performed. This work has been partially supported by DGES Grant PB98-0182-C02-01 and by the Xunta de Galicia Grant XUGA10501B97     

Estimating the Expected Probability of Misclassification for a Rule Based on the Linear Discriminant Function: Univariate Normal Case

The problem is to estimate the average probability of misclassifying an observation from a given population in the context of the two group classification problem when populations are univariate normal with unknown means and common known variance, and the rule is based on the linear discriminant function. Several estimators are compared with respect to asymptotic MSE and with respect to the distribution of the absolute error between estimator and parameter, and conclusions drawn about the best estimators.     

Studies on the Effects of Estimator Selection in Robust Parameter Design under Asymmetric Conditions

The primary goal of robust parameter design (RPD) is to determine the optimum operating conditions that achieve process performance targets while minimizing variability in the results. To achieve this goal, typical approaches to RPD problems use ordinary least squares methods to obtain response functions for the mean and variance by assuming that the experimental data follow a normal distribution and are relatively free of contaminants or outliers. Consequently, the most common estimators used in the initial tier of estimation are the sample mean and sample variance, as they are very good estimators when these assumptions hold. However, it is often the case that such assumed conditions do not exist in practice; notably, that inherent asymmetry pervades system outputs. If unaccounted for, such conditions can affect results tremendously by causing the quality of the estimates obtained using the sample mean and standard deviation to deteriorate. Focusing on asymmetric conditions, this paper examines several highly efficient estimators as alternatives to the sample mean and standard deviation. We then incorporate these estimators into RPD modeling and optimization approaches to ascertain which estimators tend to yield better solutions when skewness exists. Monte Carlo simulation and numerical studies are used to substantiate and compare the performance of the proposed methods with the traditional approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Methods for Statistical Data Analysis of Multivariate Observations

The general class of models proposed by Peña and Hollander for recurrent event data is considered under a fully parametric specification of the baseline hazard rate function and under the two cases where the model does and does not incorporate frailty components. Estimators of model parameters are presented, and their finite and asymptotic properties are ascertained. For the asymptotic properties, the results of Borgan concerning maximum likelihood estimators in counting process models are used to obtain weak convergence to Gaussian distributions of estimators. However, the required regularity conditions are reformulated into conditions involving gap times, which make it more feasible to obtain explicit theoretical expressions of asymptotic covariances. The procedures are applied to fit the general class of models with a parametric baseline hazard rate function to a dataset on hydraulic subsystems of “load-haul-dump” machines in mining.     

方差分量的非负估计

本文对含两个方差分量的线性混合模型,给出了基于谱分解估计构造方差分量的非负估计的两种新方法,由新方法构造的非负估计在一定的条件下在均方误差意义下一致优于谱分解估计,且有显式解、计算简便。     

Uniform integrability of the OLS estimators,and the convergence of their moments

The problem of convergence of moments of a sequence of random variables to the moments of its asymptotic distribution is important in many applications. These include the determination of the optimal training sample size in the cross-validation estimation of the generalization error of computer algorithms, and in the construction of graphical methods for studying dependence patterns between two biomarkers. In this paper, we prove the uniform integrability of the ordinary least squares estimators of a linear regression model, under suitable assumptions on the design matrix and the moments of the errors. Further, we prove the convergence of the moments of the estimators to the corresponding moments of their asymptotic distribution, and study the rate of the moment convergence. The canonical central limit theorem corresponds to the simplest linear regression model. We investigate the rate of the moment convergence in canonical central limit theorem proving a sharp improvement of von Bahr’s (Ann Math Stat 36:808–818, 1965) theorem.     

A comparison of three estimators of the Weibull parameters

Using mean square error as the criterion, we compare two least squares estimates of the Weibull parameters based on non‐parametric estimates of the unreliability with the maximum likelihood estimates (MLEs). The two non‐parametric estimators are that of Herd–Johnson and one recently proposed by Zimmer. Data was generated using computer simulation with three small sample sizes (5, 10 and 15) with three multiply‐censored patterns for each sample size. Our results indicate that the MLE is a better estimator of the Weibull characteristic value, θ, than the least squares estimators considered. No firm conclusions may be made regarding the best estimate of the Weibull shape parameter, although the use of maximum likelihood is not recommended for small sample sizes. Whenever least squares estimation of both Weibull parameters is appropriate, we recommend the use of the Zimmer estimator of reliability. Copyright © 2001 John Wiley & Sons, Ltd.     

A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test

We establish a joint central limit theorem for sums of squares and the fourth powers of residuals in a high-dimensional regression model. We then apply this CLT to detect the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size n tends to infinity and the number of covariates p may be fixed or tend to infinity.