Bootstrap Inference Longitudinal Semiparametric Regression Model

Semiparametric regression contains two components, i.e. parametric and nonparametric component. Semiparametric regression model is represented by y(ti) = mu((x') under tilde (ti), z(ti)) + epsilon(ti) where mu((x') under tilde (ti),z(ti)) = (x') under tilde (ti)beta + g(z(ti)), and y(ti) is response variable. It is assumed to have a linear relationship with the predictor variables (x') under tilde (ti) = (x(1i1), x(2i2), ..., x(Tir)). Random error epsilon(ti), i = 1, ..., n, t = 1, ... , T is normally distributed with zero mean and variance sigma(2) and g(z(ti)) nonparametric component. The results of this study showed that the PLS approach on longitudinal semiparametric regression models obtain estimators <(<(beta)over cap>)over tilde>(t) = [X'II(lambda)X](-1) X'II(lambda)y and <(<(g)over cap>)over tilde>lambda(z)=M(lambda)y. The result also show that bootstrap was valid on longitudinal semiparametric regression model with (g) over tilde ((b))(lambda) (z) as nonparametric component estimator.