| Generalized linear models(GLMs)play a major role in the study of regression problems where response variables are counting or classifying data,and statistical inference is based on their asymptotic theory.longitudinal data(panel data or group data)are frequently presented in biomedical,economic and social science research.Longitudinal data is the data of multiple observations of an individual is relevant,but the degree of correlation is unknown,and the observation data between different individuals is independent.generalized estimation equation(GEE)is commonly used to analyze longitudinal counting data.The empirical likelihood method(EL)has many outstanding advantages,such as constructing confidence intervals by empirical likelihood method,in addition to many advantages,such as domain retention,transformation invariance and the shape of confidence domain determined by data itself,there are Bartlett correction and no need to construct axis statistics.The empirical likelihood method is used to study the large sample property of fixed design generalized linear model under longitudinal data.Some only prove the large sample property of logarithmic empirical likelihood ratio,but not the large sample property of maximum empirical likelihood estimation.Some hypothesis conditions are not easy to verify or relatively strong in practical application.a large sample nature of log empirical likelihood ratio and maximum empirical likelihood estimation for fixed design Poisson regression models under the condition of weak and easy validation in practical applications is strictly demonstrated. |
