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1.
EMPIRICAL LIKELIHOOD RATIO CONFIDENCE INTERVALS FOR VARIOUS DIFFERENCES OF TWO POPULATIONS 总被引:1,自引:0,他引:1
Recently the empirical likelihood has been shown to be very useful in nonparametric models. Qin combined the empirical likelihood thought and the parametric likelihood method to construct confidence intervals for the difference of two population means in a semiparametric model. In this paper, we use the empirical likelihood thought to construct confidence intervals for some differences of two populations in a nonparametric model. A version of Wilks' theorem is developed. 相似文献
2.
Gran Kauermann 《Journal of multivariate analysis》2002,82(2):471
We consider the profile score function in models with smooth and parametric components. If local respectively weighted likelihood estimation is used for fitting the smooth component, the resulting profile likelihood estimate for the parametric component is asymptotically efficient as shown in T. A. Severini and W. H. Wong (1992, Ann. Statist.20, 1768–1802). However, as in solely parametric models the profile score function is not unbiased. We propose a small sample bias adjustment which results by extending the correction suggested in P. McCullagh and R. Tibshirani (1990, J. Roy. Statist. Soc. Ser. B52, 325–344) to the framework of semiparametric models. 相似文献
3.
Empirical likelihood for partial linear models 总被引:2,自引:0,他引:2
In this paper the empirical likelihood method due to Owen (1988,Biometrika,75, 237–249) is applied to partial linear random models. A nonparametric version of Wilks' theorem is derived. The theorem is
then used to construct confidence regions of the parameter vector in the partial linear models, which has correct asymptotic
coverage. A simulation study is conducted to compare the empirical likelihood and normal approximation based method.
Research supported by NNSF of China and a grant to the first author for his excellent Ph.D. dissertation work in China.
Research supported by Hong Kong RGC CERG No. HKUST6162/97P. 相似文献
4.
George R. Jerdack Pranab Kumar Sen 《Annals of the Institute of Statistical Mathematics》1990,42(1):99-114
Exact and large sample distributions of the rank order test under the null hypothesis of restricted interchangeability are obtained. Under given regularity conditions and under Pitman's shift in location alternative, the asymptotic relative efficiency of this nonparametric test in comparison with Votaw's (1948, Ann. Math. Statist., 19, 447–473) likelihood ratio test is given. 相似文献
5.
We present the score and Wald test analogues to Srivastava's (1985, Comm. Statist. A—Theory Methods, 14, 775–792) likelihood ratio tests for the multivariate growth curve model with missing data, and illustrate their use with data from an immunotherapy experiment (Fukushima et al. (1982, Int. J. Cancer, 29, 107–112, 113–117)). 相似文献
6.
Akimichi Takemura Satoshi Kuriki 《Annals of the Institute of Statistical Mathematics》1996,48(4):603-620
It is well known that likelihood ratio statistic is Bartlett correctable. We consider decomposition of a likelihood ratio statistic into 1 degree of freedom components based on sequence of nested hypotheses. We give a proof of the fact that the component likelihood ratio statistics are distributed mutually independently up to the order O(1/n) and each component is independently Bartlett correctable. This was implicit in Lawley (1956, Biometrika, 43, 295–303) and proved in Bickel and Ghosh (1990, Ann. Statist., 18, 1070–1090) using a Bayes method. We present a more direct frequentist proof. 相似文献
7.
Akio Suzukawa Hideyuki Imai Yoshiharu Sato 《Annals of the Institute of Statistical Mathematics》2001,53(2):262-276
This paper is intended as an investigation of parametric estimation for the randomly right censored data. In parametric estimation, the Kullback-Leibler information is used as a measure of the divergence of a true distribution generating a data relative to a distribution in an assumed parametric model M. When the data is uncensored, maximum likelihood estimator (MLE) is a consistent estimator of minimizing the Kullback-Leibler information, even if the assumed model M does not contain the true distribution. We call this property minimum Kullback-Leibler information consistency (MKLI-consistency). However, the MLE obtained by maximizing the likelihood function based on the censored data is not MKLI-consistent. As an alternative to the MLE, Oakes (1986, Biometrics, 42, 177–182) proposed an estimator termed approximate maximum likelihood estimator (AMLE) due to its computational advantage and potential for robustness. We show MKLI-consistency and asymptotic normality of the AMLE under the misspecification of the parametric model. In a simulation study, we investigate mean square errors of these two estimators and an estimator which is obtained by treating a jackknife corrected Kaplan-Meier integral as the log-likelihood. On the basis of the simulation results and the asymptotic results, we discuss comparison among these estimators. We also derive information criteria for the MLE and the AMLE under censorship, and which can be used not only for selecting models but also for selecting estimation procedures. 相似文献
8.
Representation theorem and local asymptotic minimax theorem are derived for nonparametric estimators of the distribution function on the basis of randomly truncated data. The convolution-type representation theorem asserts that the limiting process of any regular estimator of the distribution function is at least as dispersed as the limiting process of the product-limit estimator. The theorems are similar to those results for the complete data case due to Beran (1977, Ann. Statist., 5, 400–404) and for the censored data case due to Wellner (1982, Ann. Statist., 10, 595–602). Both likelihood and functional approaches are considered and the proofs rely on the method of Begun et al. (1983, Ann. Statist., 11, 432–452) with slight modifications.Division of Biostatistics, School of Public Health, Columbia Univ. 相似文献
9.
Detecting population (group) differences is useful in many applications, such as medical research. In this paper, we explore the probabilistic theory for identifying the quantile differences .between two populations. Suppose that there are two populations x and y with missing data on both of them, where x is nonparametric and y is parametric. We are interested in constructing confidence intervals on the quantile differences of x and y. Random hot deck imputation is used to fill in missing data. Semi-empirical likelihood confidence intervals on the differences are constructed. 相似文献
10.
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
11.
This paper mainly introduces the method of empirical likelihood and its applications on two different models. We discuss the empirical likelihood inference on fixed-effect parameter in mixed-effects model with error-in-variables. We first consider a linear mixed-effects model with measurement errors in both fixed and random effects. We construct the empirical likelihood confidence regions for the fixed-effects parameters and the mean parameters of random-effects. The limiting distribution of the empirical log likelihood ratio at the true parameter is X2p+q, where p, q are dimension of fixed and random effects respectively. Then we discuss empirical likelihood inference in a semi-linear error-in-variable mixed-effects model. Under certain conditions, it is shown that the empirical log likelihood ratio at the true parameter also converges to X2p+q. Simulations illustrate that the proposed confidence region has a coverage probability more closer to the nominal level than normal approximation based confidence region. 相似文献
12.
Andrey Feuerverger Yehuda Vardi 《Annals of the Institute of Statistical Mathematics》2000,52(1):123-138
We further explore the relation between random coefficients regression (RCR) and computerized tomography. Recently, Beran et al. (1996, Ann. Statist., 24, 2569–2592) explored this connection to derive an estimation method for the non-parametric RCR problem which is closely related to image reconstruction methods in X-ray computerized tomography. In this paper we emphasize the close connection of the RCR problem with positron emission tomography (PET). Specifically, we show that the RCR problem can be viewed as an idealized (continuous) version of a PET experiment, by demonstrating that the nonparametric likelihood of the RCR problem is equivalent to that of a specific PET experiment. Consequently, methods independently developed for either of the two problems can be adapted from one problem to the other. To demonstrate the close relation between the two problems we use the estimation method of Beran, Feuerverger and Hall for image reconstruction in PET. 相似文献
13.
Empirical likelihood (EL) was first applied to quantiles by Chen and Hall (1993,Ann. Statist.,21, 1166–1181). In this paper, we shall propose an alternative EL approach which is also some kind of the kernel method. It
not only eliminates the need to solve nonlinear equations, but also is extremely easy to implement. Confidence intervals derived
from the proposed approach are shown, by an nonparametric version of Wilks' theorem, to have the same order of coverage accuracy
(order 1/n) as those of Chen and Hall. Numerical results are presented to compare our method with other methods. 相似文献
14.
This paper proposes some diagnostic tools for checking the adequacy of multivariate regression models including classical
regression and time series autoregression. In statistical inference, the empirical likelihood ratio method has been well known
to be a powerful tool for constructing test and confidence region. For model checking, however, the naive empirical likelihood
(EL) based tests are not of Wilks’ phenomenon. Hence, we make use of bias correction to construct the EL-based score tests
and derive a nonparametric version of Wilks’ theorem. Moreover, by the advantages of both the EL and score test method, the
EL-based score tests share many desirable features as follows: They are self-scale invariant and can detect the alternatives
that converge to the null at rate n
−1/2, the possibly fastest rate for lack-of-fit testing; they involve weight functions, which provides us with the flexibility
to choose scores for improving power performance, especially under directional alternatives. Furthermore, when the alternatives
are not directional, we construct asymptotically distribution-free maximin tests for a large class of possible alternatives.
A simulation study is carried out and an application for a real dataset is analyzed.
相似文献
15.
16.
在φ混合的随机误差下,本文研究了固定设计及响应变量有缺失的非参数回归模型中回归函数的经验似然置信区间的构造.首先采用非参数回归填补法对缺失的数据进行填补,其次利用补足后得到的"完全样本"构造了非参数回归函数的经验似然比统计量,并证明了经验似然比统计量的极限分布为卡方分布,利用此结果可以构造非参数回归函数的经验似然置信区间. 相似文献
17.
Xu-Ping Zhong Bo-Cheng Wei Wing-Kam Fung 《Annals of the Institute of Statistical Mathematics》2000,52(2):367-379
In this paper, we present a unified diagnostic method for linear measurement error models based upon the corrected likelihood of Nakamura (1990, Biometrika, 77, 127–137). Both global influence and local influence are discussed. The case-deletion model and mean-shift outlier model are considered, and they are shown to be approximately equivalent. Several diagnostic measures are derived and discussed. It is found that they can be written in terms of the residual and leverage measure. Some existing results are improved. Numerical example illustrates that our method is useful for diagnosing influential observations. 相似文献
18.
Suppose that there are two nonparametric populations x and y with missing data on both of them. We are interested in constructing confidence intervals on the quantile differences of
x and y. Random imputation is used. Empirical likelihood confidence intervals on the differences are constructed.
Supported by the National Natural Science Foundation of China (No. 10661003) and Natural Science Foundation of Guangxi (No.
0728092). 相似文献
19.
Likelihood Based Confidence Intervals for the Tail Index 总被引:1,自引:0,他引:1
For the estimation of the tail index of a heavy tailed distribution, one of the well-known estimators is the Hill estimator (Hill, 1975). One obvious way to construct a confidence interval for the tail index is via the normal approximation of the Hill estimator. In this paper we apply both the empirical likelihood method and the parametric likelihood method to obtaining confidence intervals for the tail index. Our limited simulation study indicates that the normal approximation method is worse than the other two methods in terms of coverage probability, and the empirical likelihood method and the parametric likelihood method are comparable. 相似文献
20.
Tomohito Naito Kohei Asai Tomoyuki Amano Masanobu Taniguchi 《Statistical Inference for Stochastic Processes》2010,13(3):163-174
In this paper, we propose a local Whittle likelihood estimator for spectral densities of non-Gaussian processes and a local
Whittle likelihood ratio test statistic for the problem of testing whether the spectral density of a non-Gaussian stationary
process belongs to a parametric family or not. Introducing a local Whittle likelihood of a spectral density f
θ
(λ) around λ, we propose a local estimator [^(q)] = [^(q)] (l){\hat{\theta } = \hat{\theta } (\lambda ) } of θ which maximizes the local Whittle likelihood around λ, and use f[^(q)] (l) (l){f_{\hat{\theta } (\lambda )} (\lambda )} as an estimator of the true spectral density. For the testing problem, we use a local Whittle likelihood ratio test statistic
based on the local Whittle likelihood estimator. The asymptotics of these statistics are elucidated. It is shown that their
asymptotic distributions do not depend on non-Gaussianity of the processes. Because our models include nonlinear stationary
time series models, we can apply the results to stationary GARCH processes. Advantage of the proposed estimator is demonstrated
by a few simulated numerical examples. 相似文献