Efficient Estimation of a Varying-coefficient Partially Linear Binary Regression Model

This article considers a semiparametric varying-coefficient partially linear binary regressionmodel.The semiparametric varying-coefficient partially linear regression binary model which is ageneralization of binary regression model and varying-coefficient regression model that allows one toexplore the possibly nonlinear effect of a certain covariate on the response variable.A Sieve maximumlikelihood estimation method is proposed and the asymptotic properties of the proposed estimatorsare discussed.One of our main objects is to estimate nonparametric component and the unknownparameters simultaneously.It is easier to compute, and the required computation burden is much lessthan that of the existing two-stage estimation method.Under some mild conditions, the estimatorsare shown to be strongly consistent.The convergence rate of the estimator for the unknown smoothfunction is obtained, and the estimator for the unknown parameter is shown to be asymptoticallyefficient and normally distributed.Simulation studies are carried out to investigate the performance ofthe proposed method.