Statistical Analysis Of Counting Data Based On Estimating Equation

Count data widely exist in the fields of economics,finance,biomedical sciences,clinical diagnosis and industrial reliability studieds which have been paied close attention to by a large number of scholars and become a hot spot of the international statistical community recently.The research of count data is mainly focused on the study of missing values,zero-inflation problems,correlation among subjects and over-dispersion problems.Most research in panel count data has focused on the mean function parameter estimation of recurrent event process,the regression analysis and hypothesis testing.Statistical analysis of simple count data has been established based on the estimating equations.We estimate the unknown regression parameters in the model and derive the asymptotic properties of the estimators,including consistency,uniqueness and asymptotic normality.Then as applications a set of bladder cancer data has been analyzed.We illustrate the effectiveness of our proposed models under finite samples by means of numerical simulations.We proposed propensity score based on the estimation of observation process and adjust the confounding effect of observation process using the inverse probability weighting method.A semiparametric transformation model for the process of recurrent events under dependent observation process is then established,as well as eatimating equations based on the transformation model are proposed.For asympototic results,we prove the consistency and asymptotic normality of the estimators.At the end,the numerical simulations were carried out to investigate the effectiveness of the estimators under finite samples.Finally,we draw a conclusion of the main work and the theoretical results for statistical analysis of count data which present the innovativeness and the potential applications of this study and discuss ongoing work as future plan.