Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression

Ngizatul Afifah*, I. Nyoman Budiantara, I. Nyoman Latra

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

6 Citations (Scopus)


Given paired observation (xi, v1i, v2i, ⋯, vpi, t1i, t2i, ⋯, tqi, yi), i = 1, 2, ⋯, n, follow the additive semiparametric regression model yi = μ(xi, vi, ti) +i, where μ(xi,vt,ti)=f(xi)+∑j=1pgj(νji)+∑s=1qhs(tsi) vi = (v1i, v2i, ⋯, vpi), and ti = (t1i, t2i, ⋯, tqi). Random errorsi is a normal distribution with mean 0 and variance σ 2. To obtain a mixed estimator μ(xi, vi, ti), the regression curve f(xi) is approached by linier parametric, gj(vji) is kernel with bandwidths Φ = (φ1, φ2, ⋯, φp) and the regression curve component fourier series hs (tsi) 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 = (θ1, θ2, ⋯, θq), the estimator f(x) is and is , where and . So that, μΦ,θ,N(vi,ti)=Z(Φ,θ,N)y is the mixed estimator of μ(vi, ti) where Z(Φ, θ, N) = C(Φ, θ, N) + V(Φ) + E(Φ, θ, N) Matrix C(Φ, θ, N), V(Φ) and E(Φ, θ, N) are depended on Φ, θ and N. Optimal Φ, θ and N can be obtained by the smallest Generalized Cross Validation (GCV).

Original languageEnglish
Article number012002
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 12 Jun 2017
Event1st International Conference on Mathematics: Education, Theory, and Application, ICMETA 2016 - Surakarta, Indonesia
Duration: 6 Dec 20167 Dec 2016


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