Nonparametric Regression Estimation Of Homothetically Separable Functions

In econometric theory, production function, profit function and cost function have the property of homothetic. Homothetic and homothetically separable functions are commonly used to model consumer preferences and firm production, which makes the problem simpler. At the same time, additive models are widely used in econometric theory and econometric data.In this paper, some basic estimatiors of the following models are summarized: Efficient estimation of additive nonparametric regression models, efficient estimation of generzlized additive nonparametric regression models, nonparametric estimation of a generalized additive model with an unknown link function, nonparametric estimators of homothetically separable functions.Linton and Nielsen (1997) propose the method of integration. The initial value is given by integration, and then efficient estimation of additive nonparametric regression models is given by taking the initial value into one-step backfitting.Linton(1999) gives efficient estimation for generalized additive nonparametric regression models by two-step method and the linearlization of two-step estimators; by generalized additive nonparametric models and partially linear models to reduce dimensions, the nonparametric estimation with an unknown link function is propoposed; by the matching method, nonparametric estimators of homothetically separable functions is given.