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
DOIONLINE NO - IJMAS-IRAJ-DOIONLINE-7048
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Copyright: © Institute of Research and Journals
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Published on 2017-04-20 |
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