TY - JOUR

T1 - Parametric and nonparametric estimators in fourier series semiparametric regression and their characteristics

AU - Pane, Rahmawati

AU - Nyoman Budiantara, I.

AU - Zain, Ismaini

AU - Otok, Bambang Widjanarko

N1 - Publisher Copyright:
© 2014 Rahmawati Pane, I Nyoman Budiantara, Ismaini Zain and Bambang Widjanarko Otok.

PY - 2014

Y1 - 2014

N2 - Consider data pairs (xil,..., xir, til,..., tip, yi) involving in a semiparametric regression model where j=1,...,p is the semiparametric regression curve. Response variable iy is assumed to be proportional to predictor variable xi1=(xi1,.... xir ),but at the same time, its relationship with other predictor variables ti1,....,tip)is unidentified. The Xiβ and gj(tji) are, parametric and nonparametric components respectively. In this study, the nonparametric component is approximated by Fourier series which is expressed by This report also introduces the mathematical expressions of parametric estimator βλ,nonparametric estimator,ĝλ estimator for semiparametric regression curve,μλ(x,t),and their properties. The estimators are obtained from Penalized Least Square (PLS) optimization The solution of the PLS approximation produces the estimators βλ=W(λ)Y,ĝλ=M(λ)Y and μλ(x,t)=N(λ)Y for a matrices W(λ), M(λ), and N(λ), that are depending on refined parameter While βλ,ĝλand μλ(x,t) are bias estimators, which are linear with respect to observation .

AB - Consider data pairs (xil,..., xir, til,..., tip, yi) involving in a semiparametric regression model where j=1,...,p is the semiparametric regression curve. Response variable iy is assumed to be proportional to predictor variable xi1=(xi1,.... xir ),but at the same time, its relationship with other predictor variables ti1,....,tip)is unidentified. The Xiβ and gj(tji) are, parametric and nonparametric components respectively. In this study, the nonparametric component is approximated by Fourier series which is expressed by This report also introduces the mathematical expressions of parametric estimator βλ,nonparametric estimator,ĝλ estimator for semiparametric regression curve,μλ(x,t),and their properties. The estimators are obtained from Penalized Least Square (PLS) optimization The solution of the PLS approximation produces the estimators βλ=W(λ)Y,ĝλ=M(λ)Y and μλ(x,t)=N(λ)Y for a matrices W(λ), M(λ), and N(λ), that are depending on refined parameter While βλ,ĝλand μλ(x,t) are bias estimators, which are linear with respect to observation .

KW - Fourier series

KW - Penalized least square (PLS)

KW - Semiparametric regression

UR - http://www.scopus.com/inward/record.url?scp=84912050711&partnerID=8YFLogxK

U2 - 10.12988/ams.2014.46472

DO - 10.12988/ams.2014.46472

M3 - Article

AN - SCOPUS:84912050711

SN - 1312-885X

VL - 8

SP - 5053

EP - 5064

JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

IS - 101-104

ER -