ASYMPTOTIC PROPERTIES OF MLE IN EXPONENTIAL FAMILY NONLINEAR MODELS

1.IntroductionSupposethattherandomvariablesyi5y2,'',y.areindependentandeachyihasdensity:withrespecttoaa-finitemeasurev,whereb,c,]areknownl'unctions;fiisaknownq-vectordefinedinX,Pistheunknownp-vectorparameterdefinedinB,oiisthenaturalparameter,andaisascaleparameter.Then(1)iscalledtheexponentialfamilynonlinear..dels[2]whicharenaturalextensionofgeneralizedlinearmodelsandnormalnonlinearmodels.Inthispaper,wegeneralizetheasymptoticresultof[1]and[3,4]toexponentialfamilynonlinearmodels.Section2gives…     

计量经济中一类单指标模型的建模

本文基于对统计学中广义线性模型的分析、详细研究了计量经济中一类单指标模型的建模问题，提出了相应的参数估计与推断算法，并加以实施。实例分析说明该模型及其方法在实际应用中具有优越性。     

两阶段的贝叶斯模型选择与筛选试验分析

针对非正态响应的部分因子试验设计,当筛选试验所涉及的因子数目较大时,提出了一种两阶段的贝叶斯模型选择方法.首先,运用蒙特卡洛(MCMC)方法模拟广义线性模型各参数的后验分布,并根据各参数大于零或小于零的后验概率考察各变量的显著性,得到初始的当前模型与候选模型;其次,利用贝叶斯模型评估准则DIC对当前模型与候选模型进行逐步迭代优化,筛选出显著性因子,得到了具有最佳短期预测性能的模型;最后,实际的工业案例说明此方法能够有效处理非正态响应部分因子试验中显著性因子筛选问题.     

联合均值与方差模型的变量选择

在许多应用方面, 特别在经济领域和工业产品的质量改进试验中, 非常有必要对方差建模. 推广经典的正态回归模型, 对联合均值与方差模型提出一种同时对均值模型和方差模型的变量选择方法. 提出的惩罚极大似然估计具有相合性和oracle性质. 随机模拟和实例研究结果表明该模型和方法是有用和有效的.     

Statistical analysis of generalized exponential distribution under progressive censoring with binomial removals

The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented,where the number of units removed at each failure time follows a binomial distribution.Maximum likelihood estimators of the parameters and their confidence intervals are derived.The expected time required to complete the life test under this censoring scheme is investigated.Finally,the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.     

ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL

This paper addresses estimation and its asymptotics of mean transformation θ = E[h（X）] of a random variable X based on n lid. observations from errors-in-variables model Y = X＋ v, where v is a measurement error with a known distribution and h（.） is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.     

TWO-STAGE ESTIMATION FOR SEEMINGLY UNRELATED NONPARAMETRIC REGRESSION MODELS

This paper is concerned with the estimating problem of seemingly unrelated （SU） non- parametric regression models. The authors propose a new method to estimate the unknown functions, which is an extension of the two-stage procedure in the longitudinal data framework. The authors show the resulted estimators are asymptotically normal and more efficient than those based on only the individual regression equation. Some simulation studies are given in support of the asymptotic results. A real data from an ongoing environmental epidemiologie study are used to illustrate the proposed procedure.     

Testing serial correlation in semiparametric varying coefficient partially linear errors-in-variables model

The authors propose a V _{N, p} test statistic for testing finite-order serial correlation in a semiparametric varying coefficient partially linear errors-in-variables model. The test statistic is shown to have asymptotic normal distribution under the null hypothesis of no serial correlation. Some Monte Carlo experiments are conducted to examine the finite sample performance of the proposed V _{N, p} test statistic. Simulation results confirm that the proposed test performs satisfactorily in estimated size and power. This research is supported by the National Natural Science Foundation of China under Grant Nos. 10871217 and 40574003; the Science and Technology Project of Chongqing Education Committee under Grant No. KJ080609; the Doctor's Start-up Research Fund under Grant No. 08-52204; and the Youth Science Research Fund of Chongqing Technology and Business University under Grant No. 0852008.     

结合GLM与因子效应原则的贝叶斯变量选择方法

因子效应原则(效应稀疏原则、效应排序原则和效应遗传原则)经常用于评判因子设计理论与数据分析策略的合理性. 针对非正态响应的部分因子试验, 当筛选试验含有复杂的别名效应时, 提出了一种结合广义线性模型(generalized linear models, GLM)与因子效应原则的多阶段贝叶斯变量选择方法. 首先, 在广义线性模型的线性预测器中对每个变量设置一个二元变量指示器; 其次, 将因子效应原则以变量指示器的先验信息分成三个不同的阶段分别加以考虑; 然后, 利用变量指示器的后验概率识别显著性的因子效应. 最后, 仿真试验结果表明: 所提出的方法不仅能简化广义线性模型先验参数的选择, 而且能够有效地识别出非正态响应部分因子试验的显著性因子.     

连续广义系统的未知输入观测器研究

研究了在未知输入下连续广义系统的降阶观测器的设计方法,并讨论了观测器在故障检测中的应用。首先给出了连续估计器的存在条件,通过给原系统加微分反馈实现正则化,又通过解耦变换使得只有一个状态向量含有未知输入,利用其余两个不受未知输入影响的状态向量设计出观测器。然后,假设未知输入为故障信号的情况下,利用观测器的方法研究了连续广义系统的故障检测问题。仿真结果显示了满意的估计性能。     

ON WEIGHTED RANDOMLY TRIMMED MEANS

A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived. They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the heavy-tailed distributions than some other well-known location estimators; whereas the trimmed means, Winsorized means and Huber＇s M-estimator possess higher asymptotic relative efficiencies at the light-tailed distributions, in which Huber＇s M-estimator is the most robust.     

ASYMPTOTIC PROPERTIES OF L_1-NORM KERNEL ESTIMATOR OF THE CONDITIONAL MEDIAN

Let(X,Y) be a pair of R~d×R~1-valued random variables.In thispaper we investigate the asymptotic properties of the L_1-norm kernel estimator ofthe conditional median function of Y on X.Under appropriate regularity condi-tions,asymptotic normality and the optimal rates of convergence n~((-1)/(2+d))and(n~(-1)log n)~(1/(2+d)) in the L~q(1(?)q<∞)-and L~∞-norms restricted to a compactset,respectively,are obtained.Our study shows that this estimator and the well-known Nadaraya-Watson's kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.     

ADMISSIBILITY OF LINEAR ESTIMATORS OF REGRESSION COEFFICIENTS IN THE CLASS OF ALL ESTIMATORS UNDER THE MATRIX LOSS FUNCTION

For the general fixed effects linear model:Y=Xτ+ε,ε～N(0,V)(or N(0,σ~2V)),V≥0,we obtain the necessary and sufficient condition for LY+α to be admissible for Sτ in the class of allestimators under matrix loss function(d-Sτ)(d-Sτ)′;for the general random effects linear model:Y=Xβ+ε,(?)where (?)=XV_(11)X′+XV_(12)+V_(21)X′+V_(22)≥0,we also obtain the necessary and sufficient condition for LY+α to be admissible for Sα+Qβin the class of all estimators under matrix loss function(d-Sα-Qβ)(d-Sα-Qβ)′.     

ALL ADMISSIBLE LINEAR ESTIMATES OF REGRESSION COEFFICIENTS UNDER MATRIX LOSS

The necessary and sufficient conditions for a linear estimator of a linear estimable functionof regression coefficients in a general fixed effects linear model with the assumptions of normality to beadmissible in the class of all estimators under matrix liss function are given.For a general randomeffects or mixted effects linear model the necessary and sufficient conditions are obtained too.     

ON INADMISSIBILITY OF SOME USUAL ESTIMATORS OF LOSS INCURRED IN ESTIMATING ERROR VARIANCE

Under multivariant normal linear models, it is proved that usual loss estima-tors based on the uniformly minimum variance unbiased estimator and the best affinelyequivariant estimator of error variance are inadmissible with squared error loss.     

LIMIT THEOREMS AND OPTIMAL DESIGN WITH ADAPTIVE URN MODELS

In this paper we study urn model, using some available estimates of successes probabilities, and adding particle parameter, we establish adaptive models. We obtain some strong convergence theorems, rates of convergence, asymptotic normality of components in the urn, and estimates. With these asymptotical results, we show that the adaptive designs given in this paper are asymptotically optimal designs.     

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk = x'kβ g(tk) εk, 1 < k < n, where Yk's are responses, xk = (xk1,xk2,..... ,xkp)' and tk ∈T ∪R are fixed design points, β= (β1, β2, ....., βp)' is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εk is a linear process given by εk = ∑j=0∞j(?)ek-j,(?)= 1, where , are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of β, a smooth estimator of g(.), and estimators of the autocovariance and autocorrelation functions of the linear process εk.     

EXISTENCE AND UNIQUENESS OF POSITIVE EIGENVALUES FOR CERTAIN EIGENVALUE SYSTEMS

1.IntroductionLetnbeaboundeddomaininRwithsmoothboundaryoa,A.denotethep-Laplaciandefinedbya.~div(IVuIP--'Vu),forpE(1,co),andop.(u)=]nip--'if.ItiswellknownthattheeigenvalueproblemhasauniquepositiveeigenvalueAcforwhichtheeigenvalueproblerll(1.1)possessespositiveeigenfunctions.Infact,andtheeigenfunctionsforAcaretheminimizersofthefunctionalMoreover,suchaminimizerofo6Wt3'(n)existsandisuniqlle11ptoascalarmultiple,andofo6Lab(~);wenormalizeitbyjaba(x)lgholpdx~1andofo2:0inD.Thenalsoofo>0inDandcp…     

ADMISSIBILITY OF SIMULTANEOUS ESTIMATION OF SEVERAL LOSSES

In this paper,admissibility and inadmissibility results of simultaneous estimation oflosses of multivariate normal mean estimators are given.Admissible estimators for losses ofusual estimators of multivariate gamma parameters,multivariate binomial parameters andPoisson parameters are obtained respectively.