Estimation Of Single-index Panel Data Model With Fixed Effects

In this paper,we mainly study the estimation in single-index panel data models with individual effects.We transform the estimation in the single-index panel data models into partially linear single-index models by regressing the individual effect on the covariates linearly.And regardless of the individual effects are random or fixed,the conversion is valid.We consider the estimation of covariance models in Chapter 3 and consider a method to estimate the unknown regressions based on the Gener-alized Estimation of Equations(GEE).In the estimation of the wide bandwidth of non-parametric functions,our profile GEE estimates are also uniform and asymptot-ically normal even if the covariance structure is incorrectly specified.Moreover,if the covariance structure is correctly specified,the semiparametric efficiency can be ob-tained under heteroskedasticity and without assumptions distribution of covariance.In the whole estimation process,we divide it into two steps.First part,we estimate the single-index function and then bring the estimation result of single-index func-tion into the profile GEE estimation Equation,then estimate the parameters.In chapter 4,we consider how to specify the correct covariance structure under heteroscedasticity,and we consider how to estimate the parameters.Firstly,we trans-form the covariance into a binary positive semidefinite function,and decompose the binary positive semidefinite functions In the process of estimating,we are most inno-vative in constructing the covariance matrix,and we can estimate the independent components of the binary function decomposition,and finally use the estimation as the covariance matrix.Finally,we show the numerical analysis of the results.