Bootstrap inference longitudinal semiparametric regression model

Abstract

Semiparametric regression contains two components, i.e. parametric and nonparametric component. Semiparametric regression model is represented by yti=μ(x˜′ti,zti)+εti where μ(x˜′ti,zti)=x˜′tiβ˜+g(zti) and yti is response variable. It is assumed to have a linear relationship with the predictor variables x˜′ti=(x1i1,x2i2,…,xTir). Random error εti, i = 1, …, n, t = 1, …, T is normally distributed with zero mean and variance σ2 and g(zti) is a nonparametric component. The results of this study showed that the PLS approach on longitudinal semiparametric regression models obtain estimators β˜^t=[X′H(λ)X]−1X′H(λ)y˜ and g˜^λ(z)=M(λ)y˜. The result also show that bootstrap was valid on longitudinal semiparametric regression model with g^λ(b)(z) as nonparametric component estimator.