Empirical Likelihood for Generalized Linear Models with Longitudinal Data

Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.

EMPIRICAL LIKELIHOOD INFERENCE FOR LOGISTIC EQUATION WITH RANDOM PERTURBATION

Empirical likelihood(EL) combined with estimating equations(EE) provides a modern semi-parametric alternative to classical estimation techniques such as maximum likelihood estimation(MLE). This paper not only uses closed form of conditional expectation and conditional variance of Logistic equation with random perturbation to perform maximum empirical likelihood estimation(MELE) for the model parameters, but also proposes an empirical likelihood ratio statistic(ELRS) for hypotheses concerning the interesting parameter. Monte Carlo simulation results show that MELE and ELRS provide competitive performance to parametric alternatives.

Weighted quantile regression for longitudinal data using empirical likelihood

This paper proposes a new weighted quantile regression model for longitudinal data with weights chosen by empirical likelihood(EL). This approach efficiently incorporates the information from the conditional quantile restrictions to account for within-subject correlations. The resulted estimate is computationally simple and has good performance under modest or high within-subject correlation. The efficiency gain is quantified theoretically and illustrated via simulation and a real data application.

Empirical Likelihood-based Inferences in Varying Coefficient Models with Missing Data

In this paper, we consider the empirical likelihood-based inferences for varying coefficient models Y = X^τα（U） ＋ ε when X are subject to missing at random. Based on the inverse probability-weighted idea, a class of empirical log-likelihood ratios, as well as two maximum empirical likelihood estimators, are developed for α（u）. The resulting statistics are shown to have standard chi-squared or normal distributions asymptotically.Simulation studies are also constructed to illustrate the finite sample properties of the proposed statistics.

EMPIRICAL LIKELIHOOD APPROACH FOR LONGITUDINAL DATA WITH MISSING VALUES AND TIME-DEPENDENT COVARIATES

Missing data and time-dependent covariates often arise simultaneously in longitudinal studies,and directly applying classical approaches may result in a loss of efficiency and biased estimates.To deal with this problem,we propose weighted corrected estimating equations under the missing at random mechanism,followed by developing a shrinkage empirical likelihood estimation approach for the parameters of interest when time-dependent covariates are present.Such procedure improves efficiency over generalized estimation equations approach with working independent assumption,via combining the independent estimating equations and the extracted additional information from the estimating equations that are excluded by the independence assumption.The contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries.We show that the estimators are asymptotically normally distributed and the empirical likelihood ratio statistic and its profile counterpart follow central chi-square distributions asymptotically when evaluated at the true parameter.The practical performance of our approach is demonstrated through numerical simulations and data analysis.