共查询到20条相似文献,搜索用时 93 毫秒
1.
Jun Shao 《Probability Theory and Related Fields》1992,91(1):25-41
Summary This paper establishes the asymptotic normality and the consistencyrobustness of the weighted least squares estimator (WLSE) in the generalized linear models with multiple nuisance scale parameters. In addition, noting that the asymptotic robust statistical inference in presence of nuisance scale parameters requires a consistency-robust estimator of the asymptotic covariance matrix of the WLSE, this paper derives a class of covariance estimators and proves their consistency-robustness.This research was supported by an operating grant from the Natural Science and Engineering Research Council of Canada and the United States NSF-AFOSR grant ISSA-860068 相似文献
2.
The ordinary least squares estimation is based on minimization of the squared distance of the response variable to its conditional
mean given the predictor variable. We extend this method by including in the criterion function the distance of the squared
response variable to its second conditional moment. It is shown that this “second-order” least squares estimator is asymptotically
more efficient than the ordinary least squares estimator if the third moment of the random error is nonzero, and both estimators
have the same asymptotic covariance matrix if the error distribution is symmetric. Simulation studies show that the variance
reduction of the new estimator can be as high as 50% for sample sizes lower than 100. As a by-product, the joint asymptotic
covariance matrix of the ordinary least squares estimators for the regression parameter and for the random error variance
is also derived, which is only available in the literature for very special cases, e.g. that random error has a normal distribution.
The results apply to both linear and nonlinear regression models, where the random error distributions are not necessarily
known. 相似文献
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4.
The asymptotic distribution for the local linear estimator in nonparametric regression models is established under a general parametric error covariance with dependent and heterogeneously distributed regressors. A two-step estimation procedure that incorporates the parametric information in the error covariance matrix is proposed. Sufficient conditions for its asymptotic normality are given and its efficiency relative to the local linear estimator is established. We give examples of how our results are useful in some recently studied regression models. A Monte Carlo study confirms the asymptotic theory predictions and compares our estimator with some recently proposed alternative estimation procedures. 相似文献
5.
Yasunori Fujikoshi 《Journal of multivariate analysis》1985,17(1):27-37
This paper deals with two criteria for selection of variables for the discriminant analysis in the case of two multivariate normal populations with different means and a common covariance matrix. One is based on the estimated error rate of misclassification. The other uses Akaike's information criterion. The asymptotic distributions and error rate risks of the criteria are obtained. The result will prove that the two criteria are asymptotically equivalent in the sense of their asymptotic distributions and error rate risks being identical. 相似文献
6.
Linear mixed models (LMMs) have become an important statistical method for analyzing cluster or longitudinal data. In most cases, it is assumed that the distributions of the random effects and the errors are normal. This paper removes this restrictions and replace them by the moment conditions. We show that the least square estimators of fixed effects are consistent and asymptotically normal in general LMMs. A closed-form estimator of the covariance matrix for the random effect is constructed and its consistent is shown. Based on this, the consistent estimate for the error variance is also obtained. A simulation study and a real data analysis show that the procedure is effective. 相似文献
7.
In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly u... 相似文献
8.
Carlos F.A. Uchôa Francisco Cribari-Neto Tatiane A. Menezes 《European Journal of Operational Research》2014
This paper considers the issue of performing testing inference in fixed effects panel data models under heteroskedasticity of unknown form. We use numerical integration to compute the exact null distributions of different quasi-t test statistics and compare them to their limiting counterpart. The test statistics use different heteroskedasticity-consistent standard errors. Our results reveal that the asymptotic approximation is usually poor in small samples when the test statistic is based on the covariance matrix estimator proposed by Arellano (1987). The quality of the approximation is greatly increased when the standard error is obtained using other heteroskedasticity-consistent estimators, most notably the CHC4 estimator. Our results also reveal that the performance of Arellano’s test improves considerably when standard errors are computed using restricted residuals. 相似文献
9.
Yan-meng Zhao Jin-hong You Yong Zhou 《应用数学学报(英文版)》2006,22(4):565-574
A partially linear regression model with heteroscedastic and/or serially correlated errors is studied here. It is well known that in order to apply the semiparametric least squares estimation (SLSE) to make statistical inference a consistent estimator of the asymptotic covariance matrix is needed. The traditional residual-based estimator of the asymptotic covariance matrix is not consistent when the errors are heteroscedastic and/or serially correlated. In this paper we propose a new estimator by truncating, which is an extension of the procedure in White. This estimator is shown to be consistent when the truncating parameter converges to infinity with some rate. 相似文献
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11.
考虑纵向数据下混合效应EV模型。对带有惩罚项的Profile广义最小二乘方法进行了修正。利用矩估计法和ML-based EM算法给出了固定效应,随机效应以及协方差阵的估计。在一般的条件下,给出了固定效应估计的强相合性和渐近正态性,并对所提出的各种估计进行了模拟研究。模拟效果不错。 相似文献
12.
Kengo Kato 《Annals of the Institute of Statistical Mathematics》2012,64(2):255-273
We establish asymptotic normality of Powell’s kernel estimator for the asymptotic covariance matrix of the quantile regression
estimator for both i.i.d. and weakly dependent data. As an application, we derive the optimal bandwidth that minimizes the
approximate mean squared error of the kernel estimator. We also derive the corresponding results to censored quantile regression. 相似文献
13.
Many applied problems require a covariance matrix estimator that is not only invertible, but also well-conditioned (that is, inverting it does not amplify estimation error). For large-dimensional covariance matrices, the usual estimator—the sample covariance matrix—is typically not well-conditioned and may not even be invertible. This paper introduces an estimator that is both well-conditioned and more accurate than the sample covariance matrix asymptotically. This estimator is distribution-free and has a simple explicit formula that is easy to compute and interpret. It is the asymptotically optimal convex linear combination of the sample covariance matrix with the identity matrix. Optimality is meant with respect to a quadratic loss function, asymptotically as the number of observations and the number of variables go to infinity together. Extensive Monte Carlo confirm that the asymptotic results tend to hold well in finite sample. 相似文献
14.
CUI HengjianDepartment of Mathematics Statistical Data Analysis Laboratory Beijing Normal University Beijing China 《中国科学A辑(英文版)》2004,47(1):144-159
The aim of this work is to construct the parameter estimators in the partial linear errors-in-variables (EV) models and explore their asymptotic properties. Unlike other related references, the assumption of known error covariance matrix is removed when the sample can be repeatedly drawn at each designed point from the model. The estimators of interested regression parameters, and the model error variance, as well as the non-parametric function, are constructed. Under some regular conditions, all of the estimators prove strongly consistent. Meanwhile, the asymptotic normality for the estimator of regression parameter is also presented. A simulation study is reported to illustrate our asymptotic results. 相似文献
15.
Delete-group Jackknife Estimate in
Partially Linear Regression Models with Heteroscedasticity 总被引:3,自引:0,他引:3
Abstract Consider a partially linear regression model with an unknown vector parameter β,an unknownfunction g(.),and unknown heteroscedastic error variances.Chen,You proposed a semiparametric generalizedleast squares estimator(SGLSE)for β,which takes the heteroscedasticity into account to increase efficiency.Forinference based on this SGLSE,it is necessary to construct a consistent estimator for its asymptotic covariancematrix.However,when there exists within-group correlation, the traditional delta method and the delete-1jackknife estimation fail to offer such a consistent estimator.In this paper, by deleting grouped partial residualsa delete-group jackknife method is examined.It is shown that the delete-group jackknife method indeed canprovide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations.This result is an extension of that in[21]. 相似文献
16.
Jinhong You 《Journal of multivariate analysis》2006,97(4):844-873
We consider a panel data semiparametric partially linear regression model with an unknown vector β of regression coefficients, an unknown nonparametric function g(·) for nonlinear component, and unobservable serially correlated errors. The correlated errors are modeled by a vector autoregressive process which involves a constant intraclass correlation. Applying the pilot estimators of β and g(·), we construct estimators of the autoregressive coefficients, the intraclass correlation and the error variance, and investigate their asymptotic properties. Fitting the error structure results in a new semiparametric two-step estimator of β, which is shown to be asymptotically more efficient than the usual semiparametric least squares estimator in terms of asymptotic covariance matrix. Asymptotic normality of this new estimator is established, and a consistent estimator of its asymptotic covariance matrix is presented. Furthermore, a corresponding estimator of g(·) is also provided. These results can be used to make asymptotically efficient statistical inference. Some simulation studies are conducted to illustrate the finite sample performances of these proposed estimators. 相似文献
17.
Let X = (Xt, t 0) be a mean zero stationary Gaussian process with variance one, assumed to satisfy some conditions on its covariance function r. Central limit theorems and asymptotic variance formulas are provided for estimators of the square root of the second spectral moment of the process and for the number of maxima in an interval, with some applications in hydroscience. A consistent estimator of the asymptotic variance is proposed for the number of maxima. 相似文献
18.
Michael Falk 《Journal of multivariate analysis》2002,80(2):358
It is well known that the sample covariance is not an efficient estimator of the covariance of a bivariate normal vector. We extend this result to elliptical distributions and we propose a simple explicit estimator, which is efficient in the normal case and which outperforms the sample covariance in general. Necessary and sufficient conditions are established under which this estimator is in general efficient for an elliptical distribution. 相似文献
19.
崔恒建 《中国科学A辑(英文版)》2002,45(5)
This paper addresses the problem of testing goodness-of-fit for several important multivariate distributions: (Ⅰ) Uniform distribution on p-dimensional unit sphere; (Ⅱ) multivariate standard normal distribution; and (Ⅲ) multivariate normal distribution with unknown mean vector and covariance matrix. The average projection type weighted Cramér-yon Mises test statistic as well as estimated and weighted Cramér-von Mises statistics for testing distributions (Ⅰ), (Ⅱ) and (Ⅲ) are constructed via integrating projection direction on the unit sphere, and the asymptotic distributions and the expansions of those test statistics under the null hypothesis are also obtained. Furthermore, the approach of this paper can be applied to testing goodness-of-fit for elliptically contoured distributions. 相似文献
20.
A multivariate ultrastructural measurement error model is considered and it is assumed that some prior information is available in the form of exact linear restrictions on regression coefficients. Using the prior information along with the additional knowledge of covariance matrix of measurement errors associated with explanatory vector and reliability matrix, we have proposed three methodologies to construct the consistent estimators which also satisfy the given linear restrictions. Asymptotic distribution of these estimators is derived when measurement errors and random error component are not necessarily normally distributed. Dominance conditions for the superiority of one estimator over the other under the criterion of Löwner ordering are obtained for each case of the additional information. Some conditions are also proposed under which the use of a particular type of information will give a more efficient estimator. 相似文献