变系数模型变窗宽和一步局部M-估计

用变窗宽和一步局部M-估计对变系数模型的系数参数进行估计,得到了估计的渐近正态性.     

A note on constrained M-estimation and its recursive analog in multivariate linear regression models

In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a general multivariate linear regression model is considered. Since the constrained M-estimation is not easy to compute, an up-dating recursion procedure is proposed to simplify the computation of the estimators when a new observation is obtained. We show that, under mild conditions, the recursion estimates are strongly consistent. In addition, the asymptotic normality of the recursive constrained M-estimators of regression coefficients is established. A Monte Carlo simulation study of the recursion estimates is also provided. Besides, robustness and asymptotic behavior of constrained M-estimators are briefly discussed. The research was supported by the Natural Sciences and Engineering Research Council of Canada     

Estimation in additive cox models by marginal integration

Assuming an additive model on the covariate effect in proportional hazards regression, we consider the estimation of the component functions. The estimator is based on the marginal integration method. Then we use a new kind of nonparametric estimator as the pilot estimator of the marginal integration. The pilot estimator is constructed by an analogy to the two-sample problems and by appealing to the principles of local partial likelihood and local linear fitting. We derive the asymptotic distribution of the marginal integration estimator of the component functions. The result of a simulation study is also given.     

The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis

We present algorithms for singular spectrum analysis and local approximation methods used to extrapolate time series. We analyze the advantages and disadvantages of these methods and consider the peculiarities of applying them to various systems. Based on this analysis, we propose a generalization of the local approximation method that makes it suitable for forecasting very noisy time series. We present the results of numerical simulations illustrating the possibilities of the proposed method.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 148–159, January, 2005.     

An Approximate M—estimation for the Parameters of Mixed Regression Model

In this paper, to keep scale inveriance, we propose an approximate M-estrmation for the mixed regression model and show consistency of the estimation under weaker conditions than that in [1].     

Efficient and fast spline-backfitted kernel smoothing of additive models

A great deal of effort has been devoted to the inference of additive model in the last decade. Among existing procedures, the kernel type are too costly to implement for high dimensions or large sample sizes, while the spline type provide no asymptotic distribution or uniform convergence. We propose a one step backfitting estimator of the component function in an additive regression model, using spline estimators in the first stage followed by kernel/local linear estimators. Under weak conditions, the proposed estimator’s pointwise distribution is asymptotically equivalent to an univariate kernel/local linear estimator, hence the dimension is effectively reduced to one at any point. This dimension reduction holds uniformly over an interval under assumptions of normal errors. Monte Carlo evidence supports the asymptotic results for dimensions ranging from low to very high, and sample sizes ranging from moderate to large. The proposed confidence band is applied to the Boston housing data for linearity diagnosis. Supported in part by NSF awards DMS 0405330, 0706518, BCS 0308420 and SES 0127722.     

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Homogeneity of variance and correlation coefficients is one of assumptions in the analysis of longitudinal data.However, the assumption can be challenged. In this paper, we mainly propose and analyze nonlinear mixed effects models for longitudinal data with exponential correlation covariance structure, intend to introduce Huber's function in the log likelihood function and get robust estimation (M-estimation) by Fisher scoring method. Score test statistics for homogeneity of variance and correlation coefficient based on M-estimation are then studied. A simulation study is carried to assess the performance of test statistics and the method we proposed in the paper is illustrated by an actual data example.     

强混合样本且含附加信息情形M估计和分位数估计的渐近性质（英文）

在强混合样本且含附加信息情形,本文采用经验似然方法提出了一类新的M估计和新的分位数估计.结果表明,本文提出的M估计和分位数估计具有相合性和渐近正态性,且其渐近方差比一般M估计和分位数估计的渐近方差小.     

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In this paper, we apply the empirical likelihood technique to propose a new class of M-estimators and quantile estimators in the presence of some auxiliary information under strong mixing samples. It is shown that the proposed M-estimators and quantile estimators are consistent and asymptotically normally distributed with smaller asymptotic variances than those of the usual M-estimators and quantile estimators.     

Strong approximation of additive functionals

LetX ₁,X ₂,...be a sequence of i.i.d. random variables and putS ₀=0,S _n =X ₁+...+X _n . A strong approximation type result is given forA _N = _i=1 ^N f(S _i ) whereF(x),xR is a real valued function. A similar result is given for ₀ ^t g(B(s))ds. Some weak convergence type implications are also discussed.1991 Mathematics Subject Classification: Primary: 60F15, Secondary: 60J15.Supported by the Hungarian National Foundation for Scientific Research, Grant No. 1905.Supported by an NSERC Canada Grant at Carleton University.Supported by a PSC CUNY Grant No.662349.     

A survey of certain results on strong approximation by orthogonal series

This is a survey of results in a particular direction of the theory of strong approximation by orthogonal series, related mostly with author's contributions to the subject.     

Variable bandwidth and one-step local M-estimator

A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the one-step local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.     

Isomorphism of complete local noetherian rings and strong approximation

About a year ago Angus Macintyre raised the following question. Let and be complete local noetherian rings with maximal ideals and such that is isomorphic to for every . Does it follow that and are isomorphic? We show that the answer is yes if the residue field is algebraic over its prime field. The proof uses a strong approximation theorem of Pfister and Popescu, or rather a variant of it, which we obtain by a method due to Denef and Lipshitz. Examples by Gabber show that the answer is no in general.

     

两阶段串联可修系统的统计过程控制与机会维修整合研究

针对两阶段串联可修系统,研究统计过程控制(SPC)与机会维修策略整合的问题。首先,考虑系统异常因素和完全故障情形下,根据过程演变分析可能的场景,给出每个场景发生的概率;其次,基于上述场景,分析各种维修行为发生的概率;然后,考虑人力成本、生产率以及停时损失,从成本的角度,根据更新报酬理论构建整合统计过程控制与机会维修策略的成本模型;再次,采用具体实例来比较分析所提出的成本模型与单独的维修策略模型,其结果表明构建的模型在节约成本方面有着明显的优势;最后,运用分式析因设计对模型输入参数进行了敏感性分析。     

Computational aspects of robust Holt-Winters smoothing based on M-estimation

To obtain a robust version of exponential and Holt-Winters smoothing the idea of M-estimation can be used. The difficulty is the formulation of an easy-to-use recursive formula for its computation. A first attempt was made by Cipra (Robust exponential smoothing, J. Forecast. 11 (1992), 57–69). The recursive formulation presented there, however, is unstable. In this paper, a new recursive computing scheme is proposed. A simulation study illustrates that the new recursions result in smaller forecast errors on average. The forecast performance is further improved upon by using auxiliary robust starting values and robust scale estimates. This research has been supported by the Research Fund K.U. Leuven and the Fonds voor Wetenschappelijk Onderzoek (Contract number G.0594.05).     

Strong consistency of M-estimates in linear models

The strong consistency of M-estimates of the regression coefficients in a linear model under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment condition. Especially, in some important circumstances, onlyE|ψ(e_k)|^q for some q > 1 is needed, where ψ{e_k} is some score function of random error.     

Data-driven local bandwidth selection for additive models with missing data

This paper deals in the nonparametric estimation of additive models in the presence of missing data in the response variable. Specifically in the case of additive models estimated by the Backfitting algorithm with local polynomial smoothers [1]. Three estimators are presented, one based on the available data and two based on a complete sample from imputation techniques. We also develop a data-driven local bandwidth selector based on a Wild Bootstrap approximation of the mean squared error of the estimators. The performance of the estimators and the local bootstrap bandwidth selection method are explored through simulation experiments.     

On local frequencies related to farey fractions

LetP ₁ andP ₂ be two sets of prime numbers and let ω(m,P_i)=#{p: p/m, pεP_i} (i=1,2) be two related additive functions ofm. For an irreducible positive fractionm/n, defineh(m/n)=ω(m, P ₁)+ω(n, P₂). In this paper the local frequenciesv _x{h(m/n)=s}=#{m/n ∈ F_x:h(m/n)=s}/#F_x are considered, whereF _x denotes the classical Farey series. Using the mean-value theorem for multiplicative functions of rational argument, a local limit theorem forv _x{h(m/n)=s} is proved. Research supported by the Lithuanian State Science and Studies Foundation. Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 1, pp. 113–131, January–March, 2000. Translated by V. Stakènas     

左截断相依数据下非参数回归的局部M 估计

本文对左截断模型, 利用局部多项式的方法构造了非参数回归函数的局部M 估计. 在观察样本为平稳α-混合序列下, 建立了该估计量的强弱相合性以及渐近正态性. 模拟研究显示回归函数的局部M 估计比Nadaraya-Watson 型估计和局部多项式估计更稳健.