scholarly journals Empirical Likelihood for Multidimensional Linear Model with Missing Responses

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Liping Zhu
Keyword(s):  
Linear Regression ◽  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Missing Values ◽  
Probability Function ◽  
Likelihood Ratio Statistic ◽  
Selection Probability ◽  
Missing Responses ◽  
Chi Squared ◽  
Multidimensional Linear

Imputation is a popular technique for handling missing data especially for plenty of missing values. Usually, the empirical log-likelihood ratio statistic under imputation is asymptotically scaled chi-squared because the imputing data are not i.i.d. Recently, a bias-corrected technique is used to study linear regression model with missing response data, and the resulting empirical likelihood ratio is asymptotically chi-squared. However, it may suffer from the “the curse of high dimension” in multidimensional linear regression models for the nonparametric estimator of selection probability function. In this paper, a parametric selection probability function is introduced to avoid the dimension problem. With the similar bias-corrected method, the proposed empirical likelihood statistic is asymptotically chi-squared when the selection probability is specified correctly and even asymptotically scaled chi-squared when specified incorrectly. In addition, our empirical likelihood estimator is always consistent whether the selection probability is specified correctly or not, and will achieve full efficiency when specified correctly. A simulation study indicates that the proposed method is comparable in terms of coverage probabilities.

scholarly journals Empirical Likelihood for Partial Parameters in ARMA Models with Infinite Variance

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jinyu Li ◽  
Wei Liang ◽  
Shuyuan He
Keyword(s):  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Likelihood Ratio Statistic ◽  
Infinite Variance ◽  
Arma Models ◽  
Log Likelihood ◽  
Log Likelihood Ratio

This paper proposes a profile empirical likelihood for the partial parameters in ARMA(p,q)models with infinite variance. We introduce a smoothed empirical log-likelihood ratio statistic. Also, the paper proves a nonparametric version of Wilks’s theorem. Furthermore, we conduct a simulation to illustrate the performance of the proposed method.

scholarly journals Empirical Likelihood Inference for First-Order Random Coefficient Integer-Valued Autoregressive Processes

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Zhiwen Zhao ◽  
Wei Yu
Keyword(s):  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Simulation Study ◽  
Asymptotic Theory ◽  
Likelihood Ratio Statistic ◽  
Random Coefficient ◽  
Likelihood Inference ◽  
Likelihood Method ◽  
Autoregressive Processes ◽  
First Order

We apply the empirical likelihood method to estimate the variance of random coefficient in the first-order random coefficient integer-valued autoregressive (RCINAR(1)) processes. The empirical likelihood ratio statistic is derived and some asymptotic theory for it is presented. Furthermore, a simulation study is presented to demonstrate the performance of the proposed method.

scholarly journals Block Empirical Likelihood for Semiparametric Varying-Coefficient Partially Linear Errors-in-Variables Models with Longitudinal Data

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yafeng Xia ◽  
Hu Da
Keyword(s):  
Longitudinal Data ◽  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Likelihood Ratio Statistic ◽  
Likelihood Inference ◽  
Errors In Variables ◽  
Varying Coefficient ◽  
Mild Conditions ◽  
Partially Linear ◽  
Log Likelihood

Block empirical likelihood inference for semiparametric varying-coeffcient partially linear errors-in-variables models with longitudinal data is investigated. We apply the block empirical likelihood procedure to accommodate the within-group correlation of the longitudinal data. The block empirical log-likelihood ratio statistic for the parametric component is suggested. And the nonparametric version of Wilk’s theorem is derived under mild conditions. Simulations are carried out to access the performance of the proposed procedure.

Weighted-Correct Empirical likelihood for Linear EV Models

2012 ◽  
Vol 524-527 ◽  
pp. 3884-3887
Author(s):  
Yu Ying Jiang ◽  
Xiao Feng Zhu
Keyword(s):  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Estimation Procedure ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Chi Square ◽  
Missing Responses ◽  
Ev Model

The empirical likelihood inference based weighted correction in linear EV model with missing responses is studied. A weighted-correct empirical likelihood method is developed. It can be shown that the weighted-correct empirical likelihood ratio is asymptotically standard chi-square. The results can be used directly to construct the asymptotic confidence regions of the unknown parameters. The estimation procedure is relatively simple and the estimated efficiency has been greatly improved.

Empirical Likelihood Inference for Linear EV Models with Missing Responses Problem

2012 ◽  
Vol 482-484 ◽  
pp. 1999-2002 ◽  
Author(s):  
Qiang Liu
Keyword(s):  
Confidence Intervals ◽  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Simulation Study ◽  
Likelihood Inference ◽  
Chi Square ◽  
Missing Responses ◽  
Adjusted Empirical Likelihood ◽  
Coverage Probabilities ◽  
Ev Model

The empirical likelihood inference for linear EV model with missing responses problem is studied. An adjusted empirical likelihood is developed. It can be shown that the adjusted empirical likelihood ratio is asymptotically standard chi-square. Simulation study indicates that the proposed method performs competitively in terms of the average lengths and coverage probabilities of confidence intervals.

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