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.

scholarly journals Interval Estimation of Random Coefficient Integer-Valued Autoregressive Model Based on Mean Empirical Likelihood Method

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xianghong Xu ◽  
Dehui Wang ◽  
Zhiwen Zhao
Keyword(s):  
Data Analysis ◽  
Empirical Likelihood ◽  
Autoregressive Model ◽  
Interval Estimation ◽  
Real Data ◽  
Confidence Regions ◽  
Random Coefficient ◽  
Likelihood Method ◽  
First Order ◽  
The Mean

In this paper, we study the use of the mean empirical likelihood (MEL) method in a first-order random coefficient integer-valued autoregressive model. The MEL ratio statistic is established, its limiting properties are discussed, and the confidence regions for the parameter of interest are derived. Furthermore, a simulation study is presented to demonstrate the performance of the proposed method. Finally, a real data analysis of dengue fever is performed.

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.

Empirical likelihood test for a large-dimensional mean vector

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 591-607
Author(s):  
Xia Cui ◽  
Runze Li ◽  
Guangren Yang ◽  
Wang Zhou
Keyword(s):  
Covariance Matrix ◽  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Sample Covariance Matrix ◽  
Likelihood Method ◽  
Numerical Comparison ◽  
Ratio Test ◽  
Empirical Likelihood Ratio ◽  
Sample Covariance ◽  
Empirical Likelihood Ratio Test

Summary This paper is concerned with empirical likelihood inference on the population mean when the dimension $p$ and the sample size $n$ satisfy $p/n\rightarrow c\in [1,\infty)$. As shown in Tsao (2004), the empirical likelihood method fails with high probability when $p/n>1/2$ because the convex hull of the $n$ observations in $\mathbb{R}^p$ becomes too small to cover the true mean value. Moreover, when $p> n$, the sample covariance matrix becomes singular, and this results in the breakdown of the first sandwich approximation for the log empirical likelihood ratio. To deal with these two challenges, we propose a new strategy of adding two artificial data points to the observed data. We establish the asymptotic normality of the proposed empirical likelihood ratio test. The proposed test statistic does not involve the inverse of the sample covariance matrix. Furthermore, its form is explicit, so the test can easily be carried out with low computational cost. Our numerical comparison shows that the proposed test outperforms some existing tests for high-dimensional mean vectors in terms of power. We also illustrate the proposed procedure with an empirical analysis of stock data.

Statistical inference for Markov processes when the model is incorrect

1979 ◽  
Vol 11 (04) ◽  
pp. 737-749
Author(s):  
Robert V. Foutz ◽  
R. C. Srivastava
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Likelihood Ratio ◽  
Markov Processes ◽  
Transition Probability ◽  
Likelihood Ratio Statistic ◽  
Null Distribution ◽  
Transition Density ◽  
Likelihood Method ◽  
Incorrect Model

Statistical inference for Markov processes is commonly based on the maximum likelihood method of estimation and the likelihood ratio criterion for testing hypotheses. Construction of estimators and test statistics by these methods require that a model be chosen in the form of a family of transition density functions. In this paper, asymptotic properties of the maximum likelihood estimator and of the likelihood ratio statistic λ n are examined when the model chosen for their construction is incorrect—that is, when no density in the model is a density for the transition probability distribution of the Markov process. It is shown that if and λ n are constructed from a ‘regular’ incorrect model, then is consistent and asymptotically normally distributed and the asymptotic null distribution of −2 log λ n is that of a linear combination of independent chi-squared random variables. These results are applied to propose measures of the performance of the test based on λ n when the statistic is constructed from an incorrect model.

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