共查询到20条相似文献,搜索用时 31 毫秒
1.
Naoto Kunitomo 《Annals of the Institute of Statistical Mathematics》1987,39(1):575-591
Summary The maximum likelihood (ML) estimator and its modification in the linear functional relationship model with incidental parameters
are shown to be third-order asymptotically efficient among a class of almost median-unbiased and almost mean-unbiased estimators,
respectively, in the large sample sense. This means that the limited information maximum likelihood (LIML) estimator in the
simultaneous equation system is third-order asymptotically efficient when the number of excluded exogenous variables in a
particular structural equation is growing along with the sample size. It implies that the LIML estimator has an optimum property
when the system of structural equations is large.
The research was partly supported by National Science Foundation Grant SES 79-13976 at the Institute for Mathematical Studies
in the Social Sciences, Stanford University and Grant-in-Aid 60301081 of the Ministry of Education, Science and Culture at
the Faculty of Economics, University of Tokyo. This paper was originally written as a part of the author's Ph.D. dissertation
submitted to Stanford University in August, 1981. Some details of the paper were deleted at the suggestion of the associate
editor of this journal. 相似文献
2.
3.
Jun Shao 《Annals of the Institute of Statistical Mathematics》1992,44(4):673-686
In a generalized linear model, the jackknife estimator of the asymptotic covariance matrix of the maximum likelihood estimator is shown to be consistent. The corresponding jackknife studentized statistic is asymptotically normal. In addition, these results remain true even if there exist unequal dispersion parameters in the model. On the other hand, the variance estimator and the studentized statistic based on the standard method (substitution and linearization) do not enjoy this robustness property against the presence of unequal dispersion parameters.This research was supported by an Operating Grant from the Natural Science and Engineering Research Council of Canada. 相似文献
4.
This article considers a semiparametric varying-coefficient partially linear regression model with current status data. 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 maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach. 相似文献
5.
In this article we study the empirical likelihood inference for MA(q) model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parameter, and we also propose an empirical log-likelihood ratio based on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotical standard chi-square distribution. 相似文献
6.
ZhiYanXU WeiAnZHENG 《数学学报(英文版)》2005,21(2):303-314
We consider the maximum likelihood estimator of the unknown parameter in a class of nonstationary diffusion processes. We give further a precise estimate for the error of the estimator. 相似文献
7.
Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence
estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence
estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper,
three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of
weighted estimators. Simplified close-form solutions are found, which always outperform the working independence estimator.
We also prove that the working independence estimator has high statistical efficiency, when asymptotic covariance of derivatives
of partial log-likelihood functions is nearly exchangeable or diagonal. Simulations are conducted to compare the performance
of the weighted estimator and working independence estimator. A data set from Busselton population health surveys is analyzed
using the proposed estimators.
This work was supported by National Natural Science Foundation of China (Grant No. 10628104), Fan was also supported by National
Institutes of Health (Grant No. R01-GM072611) and Natural Science Foundation (Grant No. DMS-0714554), Zhou was supported by
National Natural Science Funds for Distinguisheel Young Scholar (Grant No. 70825004), National Natural Science Foundation
of China (Grant Nos. 10731010, 10628104), the National Basic Research Program (Grant No. 2007CB814902), Creative Research
Groups of China (Grant No. 10721101) and Leading Academic Disipline Program, the 10
th
five year plan of 211 Project for Shanghai University of Finance and Economics (the 3
rd
phase), Cai was supported by National Institutes of Health (Grant No. R01-HL57444) 相似文献
8.
On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes
We consider the problem of the construction of the asymptotically distribution free test by the observations of ergodic diffusion process. It is supposed that under the basic hypothesis the trend coefficient depends on a finite-dimensional parameter and we study the Cramér-von Mises type statistics. The underlying statistics depends on the deviation of the local time estimator from the invariant density with parameter replaced by the maximum likelihood estimator. We propose a linear transformation which yields the convergence of the test statistics to an integral of the Wiener process. Therefore the test based on this statistics is asymptotically distribution free. 相似文献
9.
A problem of goodness-of-fit test for ergodic diffusion processes is presented. In the null hypothesis the drift of the diffusion is supposed to be in a parametric form with unknown shift parameter. Two Cramer–von Mises type test statistics are studied. The first test uses the local time estimator of the invariant density, the second one uses the empirical distribution function. The unknown parameter is estimated via the maximum likelihood estimator. It is shown that the limit distribution of the two test statistics does not depend on the unknown parameter, thus both the tests are asymptotically parameter free. Some considerations on the consistency of the proposed tests and some simulation studies are also given. 相似文献
10.
Kai Fun Yu 《Journal of Theoretical Probability》1989,2(2):193-199
A sequential procedure is proposed to determine the sample size for a fixed-width confidence interval for an unknown parameter with its maximum likelihood estimator as the center of the interval. It is established that the sequential procedure is asymptotically consistent and efficient. 相似文献
11.
Zhensheng Huang Zhangong Zhou Rong Jiang Weimin Qian Riquan Zhang 《Statistics & probability letters》2010,80(5-6):497-504
This paper considers statistical inference for semiparametric varying coefficient partially linear models with error-prone linear covariates. An empirical likelihood based statistic for parametric component is developed to construct confidence regions. The resulting statistic is shown to be asymptotically chi-square distributed. By the empirical likelihood ratio function, the maximum empirical likelihood estimator of the parameter is defined and the asymptotic normality is shown. A simulation experiment is conducted to compare the empirical likelihood, normal based and the naive empirical likelihood methods in terms of coverage accuracies of confidence regions. 相似文献
12.
This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ22 null limiting distribution. 相似文献
13.
This article concerded with a semiparametric generalized partial linear model (GPLM) with the type Ⅱ censored data. A sieve maximum likelihood estimator (MLE) is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate. 相似文献
14.
Ching-Yuan Chiang Madan L. Puri 《Annals of the Institute of Statistical Mathematics》1984,36(1):35-50
Summary In the linear regression modelX
i=α+βci+Zi, we consider the problem of testing the subhypothesis that some (but not all) components of β are equal to 0. A class of
asymptotically distribution-free tests based on a quadratic form in aligned rank statistic is studied and the asymptotic relative
efficiencies of the proposed tests with respect to the general likelihood ratio test and the test based on least-squares estimates
of regression parameters are derived. Asymptotic optimality (à la Wald) is also discussed.
Work done under the National Science Foundation Grant MCS 8301409 and NATO Grant 1465. 相似文献
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16.
Empirical likelihood inference for parametric and nonparametric parts in functional coefficient ARCH-M models is investigated in this paper. Firstly, the kernel smoothing technique is used to estimate coefficient function δ(x). In this way we obtain an estimated function with parameter β.Secondly, the empirical likelihood method is developed to estimate the parameter β. An estimated empirical log-likelohood ratio is proved to be asymptotically standard chi-squred, and the maximum empirical likelihood estimation(MELE) for β is shown to be asymptotically normal. Finally, based on the MELE of β, the empirical likelihood approach is again applied to reestimate the nonparametric part δ(x). The empirical log-likelohood ratio for δ(x) is proved to be also asymptotically standard chi-squred. Simulation study shows that the proposed method works better than the normal approximation method in terms of average areas of confidence regions for β, and the empirical likelihood confidence belt for δ(x) performs well. 相似文献
17.
In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chi-square distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best. 相似文献
18.
Hironori Fujisawa 《Journal of multivariate analysis》2003,86(1):126-142
The conditional maximum likelihood estimator is suggested as an alternative to the maximum likelihood estimator and is favorable for an estimator of a dispersion parameter in the normal distribution, the inverse-Gaussian distribution, and so on. However, it is not clear whether the conditional maximum likelihood estimator is asymptotically efficient in general. Consider the case where it is asymptotically efficient and its asymptotic covariance depends only on an objective parameter in an exponential model. This remand implies that the exponential model possesses a certain parallel foliation. In this situation, this paper investigates asymptotic properties of the conditional maximum likelihood estimator and compares the conditional maximum likelihood estimator with the maximum likelihood estimator. We see that the bias of the former is more robust than that of the latter and that two estimators are very close, especially in the sense of bias-corrected version. The mean Pythagorean relation is also discussed. 相似文献
19.
Adam T. Martinsek 《Annals of the Institute of Statistical Mathematics》1989,41(3):521-540
A sequential procedure is proposed for constructing a fixed-size confidence region for the parameters of a linear regression model. The procedure is based on certain regression analogues of trimmed means, as formulated by Welsh (1987,Ann. Statist.,15, 20–36), rather than least squares estimates. For error distributions with continuous, symmetric density and some moment higher than fourth finite, if the design points of the model are bounded, then the procedure is both asymptotically consistent and asymptotically efficient as the size of the region approaches zero.Research supported in part by the National Science Foundation under Grants DMS 85-03321 and 88-02556 and by the Air Force under Grant AFOSR-87-0041. 相似文献
20.
In this article we study the empirical likelihood inference for AR(p) model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parametric, and we also propose an empirical log-likelihood ratio base on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotically standard chi-squared. 相似文献