Paper Title :Mixed Estimator of Kernel and Fourier Series in Nonparametric Regression

Author :Ngizatul Afifah, I Nyoman Budiantara, I Nyoman Latra

Article Citation :Ngizatul Afifah ,I Nyoman Budiantara ,I Nyoman Latra , (2017 ) " Mixed Estimator of Kernel and Fourier Series in Nonparametric Regression " , International Journal of Management and Applied Science (IJMAS) , pp. 71-76, Volume-3,Issue-2

Abstract : Lets paired the observation  v 1 i , v 2 i , ..., v pi , t 1 i , t 2 i , ..., t qi , y i  , i  1, 2,..., n , follow the additive nonparametric   v i , t i    i , where   v regression model y i  p , t i   i q  g  v    h  t  , j ji s j  1 si s  1 v i   v 1 i , v 2 i ,..., v pi   , and t i   t 1 i , t 2 i ,..., t qi   . Random errors  i is a normal distribution with mean 0 and variance  2 . The aim of this study is obtain a mixed estimator   v , t  . In order to accomplish the aim, the regression i Φ    1 ,  2 ,  ,  p   and the regression curve component   curve g j v ji is approached by kernel with bandwidths h s  t si  is fourier series where it is approached by T s  t si   b s t si  p p The estimator  g  v  j ji is 1 2 M a 0 s   a ks cos kt si with oscillation paremeter M. k  1 p  g ˆ  v  j  j ji where j  1 j  1 i  g ˆ  v   V  Φ  y . j  j Based on Penalized Least Squares (PLS) ji j  1 method  q Min R  a   a s s si s  1 q  h ˆ    J  T  t   with smoothing parameter λ    1 ,  2 ,  ,  q   , q the estimator  h  t  s si is s  1 q  s , M  t  , si and s  1  h ˆ  s , M  t   Xa ˆ  λ  . So that, the mixed estimator μ  v , t  si i i is s  1 μ ˆ Φ , λ , M  v i , t i   Z  Φ , λ , M  y       where Z Φ , λ , M y  V Φ  S Φ , λ , M   y .   Matrix V Φ  and S Φ , λ , M parameter Φ , smoothing parameter λ and oscillation paremeter M. Optimal Generalized Cross Validation (GCV).  are depended on bandwidths Φ , λ and M can be obtained by using Keywords- Mixed Nonparametric Regression, Kernel, Fourier Series

Type : Research paper

Published : Volume-3,Issue-2

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