THE ASYMPTOTIC DISTRIBUTIONS OF EMPIRICAL LIKELIHOOD RATIO STATISTICS IN THE PRESENCE OF MEASUREMENT ERROR

Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.

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 CONFIDENCE REGION FOR PARAMETERS IN LINEAR ERRORS-IN-VARIABLES MODELS WITH MISSING DATA

The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.

Empirical Likelihood Based Diagnostics for Heteroscedasticity in Semiparametric Varying-Coefficient Partially Linear Models with Missing Responses

This paper proposes an empirical likelihood based diagnostic technique for heteroscedasticity for semiparametric varying-coefficient partially linear models with missing responses. Firstly, the authors complement the missing response variables by regression method. Then, the empirical likelihood method is introduced to study the heteroscedasticity of the semiparametric varying-coefficient partially linear models with complete-case data. Finally, the authors obtain the finite sample property by numerical simulation.

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.

Empirical likelihood inference for semi-parametric estimating equations

Qin and Lawless (1994) established the statistical inference theory for the empirical likelihood of the general estimating equations. However, in many practical problems, some unknown functional parts h(t) appear in the corresponding estimating equations EFG(X, h(T), β) = 0. In this paper, the empirical likelihood inference of combining information about unknown parameters and distribution function through the semiparametric estimating equations are developed, and the corresponding Wilk's theorem is established. The simulations of several useful models are conducted to compare the finite-sample performance of the proposed method and that of the normal approximation based method. An illustrated real example is also presented.