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1.
Summary This paper establishes the uniform closeness of a weighted residual empirical process to its natural estimate in the linear regression setting when the errors are Gaussian, or a function of Gaussian random variables, that are strictly stationary and long range dependent. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with long range dependent errors. The latter result, in turn, yields the asymptotic distribution of the Jaeckel (1972) rank estimators. The paper also studies the least absolute deviation and a class of certain minimum distance estimators of regression parameters and the kernel type density estimators of the marginal error density when the errors are long range dependent.Research of this author was partly supported by the NSF grant: DMS-9102041  相似文献   

2.
This paper studies local M-estimation of the nonparametric components of additive models.A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives.Under very mild conditions,the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known.The established asymptotic results also hold for two particular local M-estimations:the local least squares and least absolute deviation estimations.However,for general two-stage local M-estimation with continuous and nonlinear ψ-functions,its implementation is time-consuming.To reduce the computational burden,one-step approximations to the two-stage local M-estimators are developed.The one-step estimators are shown to achieve the same effciency as the fully iterative two-stage local M-estimators,which makes the two-stage local M-estimation more feasible in practice.The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers.In addition,the practical implementation of the proposed estimation is considered in details.Simulations demonstrate the merits of the two-stage local M-estimation,and a real example illustrates the performance of the methodology.  相似文献   

3.
This article considers a semiparametric varying-coefficient partially linear regression model.The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are discussed.Our main object is to estimate the nonparametric component and the unknown parameters simultaneously.It is easier to compute and the required computation burden is much less than the existing two-stage estimation method.Furthermore,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ( ).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed.Numerical experiments are carried out to investigate the performance of the proposed method.  相似文献   

4.
We study a multivariate ultrastructural measurement error (MUME) model with more than one response variable. This model is a synthesis of multivariate functional and structural models. Three consistent estimators of regression coefficients, satisfying the exact linear restrictions have been proposed. Their asymptotic distributions are derived under the assumption of a non-normal measurement error and random error components. A simulation study is carried out to investigate the small sample properties of the estimators. The effect of departure from normality of the measurement errors on the estimators is assessed.  相似文献   

5.
A linear functional errors-in-variables model with unknown slope parameter and Gaussian errors is considered. The measurement error variance is supposed to be known, while the variance of errors in the equation is unknown. In this model a risk bound of asymptotic minimax type for arbitrary estimators is established. The bound lies above that one which was found previously in the case of both variances known. The bound is attained by an adjusted least-squares estimators.  相似文献   

6.
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  相似文献   

7.
The purpose of this paper is to investigate the asymptotic properties of the least squares estimates (L 2-estimates) and the least absolute deviation estimates (L 1-estimates) of the parameters of a nonlinear regression model subject to a set of equality and inequality restrictions, which has a long-range dependent stationary process as its stochastic errors. Then we will compare the asymptotic relative efficiencies of the above estimators.  相似文献   

8.
There is a good deal of literature that investigates the properties of various operational variants of Theil's (1971, Principles of Econometrics, Wiley, New York) minimum mean squared error estimator. It is interesting that virtually all of the existing analysis to date is based on the premise that the model's disturbances are i.i.d., an assumption which is not satisfied in many practical situations. In this paper, we consider a model with non-spherical errors and derive the asymptotic distribution, bias and mean squared error of a general class of feasible minimum mean squared error estimators. A Monte-Carlo experiment is conducted to examine the performance of this class of estimators in finite samples.  相似文献   

9.
In this paper, we define two restricted estimators for the regression parameters in a multiple linear regression model with measurement errors when prior information for the parameters is available. We then construct two sets of improved estimators which include the preliminary test estimator, the Stein-type estimator and the positive rule Stein type estimator for both slope and intercept, and examine their statistical properties such as the asymptotic distributional quadratic biases and the asymptotic distributional quadratic risks. We remove the distribution assumption on the error term, which was generally imposed in the literature, but provide a more general investigation of comparison of the quadratic risks for these estimators. Simulation studies illustrate the finite-sample performance of the proposed estimators, which are then used to analyze a dataset from the Nurses Health Study.  相似文献   

10.
In this paper, we consider a linear mixed-effects model with measurement errors in both fixed and random effects and find the moment of estimators for the parameters of interest. The strong consistency and asymptotic normality of the estimators are obtained under regularity conditions. Moreover, we obtain the strong consistent estimators of the asymptotic covariance matrices involved in the limiting theory. Simulations are reported for illustration.  相似文献   

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