2017 : Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression

Drs. I Nyoman Latra M.Sc
Prof. Dr. Drs. I Nyoman Budiantara M.Si


Given paired observation (x i, v 1i, v 2i,..., v pi, t 1i, t 2i,..., t qi, y i), i= 1, 2,..., n, follow the additive semiparametric regression model y i= μ (x i, v i, t i)+ epsilon i, where μ (xi, vt, ti)= f (xi)+∑ j= 1pgj (νji)+∑ s= 1qhs (tsi) v i=(v 1i, v 2i,..., v pi)', and t i=(t 1i, t 2i,..., t qi)'. Random errors epsilon i is a normal distribution with mean 0 and variance σ 2. To obtain a mixed estimator μ (x i, v i, t i), the regression curve f (x i) is approached by linier parametric, g j (v ji) is kernel with bandwidths Φ=(phiv 1, phiv 2,..., phiv p)'and the regression curve component fourier series h s (t si) is approached by with oscillation paremeter N. The estimator is where . Penalized Least Squares (PLS) method give Minc, β {L (c)+ L (β)+∑ s= 1qθsS (Hs (tsi))} with smoothing parameter θ=(θ 1, θ 2,..., θ q)', the estimator f (x) is and is , where and …