scholarly journals Generalized empirical likelihood methods for analyzing longitudinal data

Biometrika ◽  
2010 ◽  
Vol 97 (1) ◽  
pp. 79-93 ◽  
Author(s):  
Suojin Wang ◽  
Lianfen Qian ◽  
Raymond J. Carroll
Keyword(s):  
Longitudinal Data ◽  
Empirical Likelihood ◽  
Simulation Study ◽  
Normal Approximation ◽  
Efficient Estimation ◽  
Likelihood Method ◽  
Finite Sample ◽  
Estimation Of Parameters ◽  
Generalized Empirical Likelihood ◽  
Study Results

Abstract Efficient estimation of parameters is a major objective in analyzing longitudinal data. We propose two generalized empirical likelihood-based methods that take into consideration within-subject correlations. A nonparametric version of the Wilks theorem for the limiting distributions of the empirical likelihood ratios is derived. It is shown that one of the proposed methods is locally efficient among a class of within-subject variance-covariance matrices. A simulation study is conducted to investigate the finite sample properties of the proposed methods and compares them with the block empirical likelihood method by You et al. (2006) and the normal approximation with a correctly estimated variance-covariance. The results suggest that the proposed methods are generally more efficient than existing methods that ignore the correlation structure, and are better in coverage compared to the normal approximation with correctly specified within-subject correlation. An application illustrating our methods and supporting the simulation study results is presented.

scholarly journals Empirical Likelihood Estimation for Population Pharmacokinetic Study Based on Generalized Linear Model

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Fang-rong Yan ◽  
Jin-guan Lin ◽  
Yuan Huang ◽  
Jun-lin Liu ◽  
Tao Lu
Keyword(s):  
Linear Model ◽  
Empirical Likelihood ◽  
Pharmacokinetic Study ◽  
Generalized Linear Model ◽  
Efficient Estimation ◽  
Likelihood Method ◽  
Population Pharmacokinetic ◽  
Pharmacokinetic Data ◽  
Population Pharmacokinetic Study ◽  
Study Results

To obtain efficient estimation of parameters is a major objective in population pharmacokinetic study. In this paper, we propose an empirical likelihood-based method to analyze the population pharmacokinetic data based on the generalized linear model. A nonparametric version of the Wilk's theorem for the limiting distributions of the empirical likelihood ratio is derived. Simulations are conducted to demonstrate the accuracy and efficiency of empirical likelihood method. An application illustrating our methods and supporting the simulation study results is presented. The results suggest that the proposed method is feasible for population pharmacokinetic data.

scholarly journals Empirical Likelihood in Nonignorable Covariate-Missing Data Problems

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Yanmei Xie ◽  
Biao Zhang
Keyword(s):  
Missing Data ◽  
Empirical Likelihood ◽  
Probability Model ◽  
Estimating Equations ◽  
Regression Function ◽  
Efficient Estimation ◽  
Likelihood Method ◽  
Finite Sample ◽  
Data Set ◽  
Working Models

Abstract:Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. We study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. We adopt the semiparametric perspective of Bartlett et al. (Improving upon the efficiency of complete case analysis when covariates are MNAR. Biostatistics 2014;15:719–30) on regression analyses with nonignorable missing covariates, in which they have introduced the use of two working models, the working probability model of missingness and the working conditional score model. In this paper, we study an empirical likelihood approach to nonignorable covariate-missing data problems with the objective of effectively utilizing the two working models in the analysis of covariate-missing data. We propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. One useful feature of these unbiased estimating equations is that they naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. We apply the general methodology of empirical likelihood to optimally combine these unbiased estimating equations. We propose three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. We present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. The proposed empirical likelihood method is also illustrated by an analysis of a data set from the US National Health and Nutrition Examination Survey (NHANES).

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 Estimation for Non-Gaussian Locally Stationary Processes with Empirical Likelihood Method

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Hiroaki Ogata
Keyword(s):  
Empirical Likelihood ◽  
Numerical Study ◽  
Asymptotic Distributions ◽  
Likelihood Method ◽  
Stationary Processes ◽  
Finite Sample ◽  
Empirical Likelihood Method ◽  
Locally Stationary Processes ◽  
Non Gaussian ◽  
Maximum Empirical Likelihood Estimator

An application of the empirical likelihood method to non-Gaussian locally stationary processes is presented. Based on the central limit theorem for locally stationary processes, we give the asymptotic distributions of the maximum empirical likelihood estimator and the empirical likelihood ratio statistics, respectively. It is shown that the empirical likelihood method enables us to make inferences on various important indices in a time series analysis. Furthermore, we give a numerical study and investigate a finite sample property.

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