L-1-estimation in a semiparametric model with longitudinal data

摘要

Consider the semiparametric model Y-ij=X-i(T)beta 0+g(t(ij))+e(ij), where beta(0) is a k x 1 vector of unknown parameters, g(.) is a function to be estimated and e(ij) are unobserved disturbances. A piecewise polynomial is proposed to approximate g and two least absolute deviation estimators of beta(0) are obtained by using two weighting schemes: equal weight for each subject and equal weight for each measurement. Two local least absolute deviation estimators of g(.) are also obtained by replacing beta(0) in this model with their least absolute deviation estimators and using a local linear approximation. The asymptotic distributions of the estimators of beta(0) are derived. The asymptotic distributions of the local least absolute deviation estimators of g(.) at both interior and boundary points are also established. Finite sample properties of our procedures are studied through Monte Carlo simulations.