Introduction

Abstract

A partially linear regression model of the form is defined by $$ {Y_i} = X_i^T\beta + g\left( {{T_i}} \right) + {\varepsilon_i},i = 1,...,n $$ (1.1.1) where X i =(x i1 ,...,x ip ) Tand T i =(t i1 ,...,t id ) T are vectors of explanatory variables, (X i ,T i ) are either independent and identically distributed (i.i.d.) random design points or fixed design points. β = (β 1 ,…, β p ) T is a vector of unknown parameters, g is an unknown function from ℝ;d to ℝ1, and ε1, …, εn are independent random errors with mean zero and finite variances of (Math)\( \sigma_i^2 = E\varepsilon 2_i^2 \) KeywordsDesign PointParametric ComponentNonparametric ComponentPositive Weight FunctionPenalize Little SquareThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.