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 βλλand μλ(x,t) are bias estimators, which are linear with respect to observation .

Original languageEnglish
Pages (from-to)5053-5064
Number of pages12
JournalApplied Mathematical Sciences
Issue number101-104
Publication statusPublished - 2014


  • Fourier series
  • Penalized least square (PLS)
  • Semiparametric regression


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