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 -