ESTIMASI MODEL REGRESI NONPARAMETRIK MENGGUNAKAN RADIAL SMOOTHING BERDASARKAN ESTIMATOR PENALIZED SPLINE
Abstract: Regression
analysis is one of statistic
methods that describes the
relationship between
predictor variable and
response variable. with
two responses variable
which correlate each other
is called biresponse
regression. Generally, the
model of nonparametric regression
is π§π= π
π¦π+
ππ, i
= 1,2,...,n.Where π§πis response
variable observatiaon to i, π¦πis predictor
variable observation to i, and ππis error random
with mean 0 and
varians π2. One
of smoothing technik
use for estimate
the nonparametric model is
using radial smoothing based on
Penalized Spline Estimator. To get optimum lambda and
optimum knot number
is done by
minimized GCV ( Generalized
Cross Validation) based from
Demmler – Reinsch
Ortogonalization algorithm. A
form of estimation of
nonparametric regression model with radial smoothing based on penalized spline
estimator is π = π« π«πΌπ«
+ ππ¬−ππ«πΌπ. The estimation of nonparametric regression model with
radial smoothing based
on penalized spline
applied to the
data of Indeks Harga
Konsumen (IHK) and
inflasi bulanan Indonesia
tahun 2006 –
2011. Response variable is Indeks Harga
Konsumen (IHK) and
predictor variable is
Inflasi Bulanan. Based from the
estimation models, the value of minimized GCV is 27.05262 with knot number is 7
and optimum lambda is 7.906043. output Kolmogorov-Smirnov test with π½
= 0.05 about error (π) have a result p-value = 0.0942. Because of
p-value > π½, H0
accepted. With the result proved that error (π)
is normal distribution with mean
-1.712044e-013 and varians 0.4840309.
output Kolmogorov-Smirnov test with = 0.05 about random effect(u) have
a result p-value
= 0.5. Because
of p-value > π½, H0
accepted. With the
result proved that error (π) is normal distribution
with mean 0.03410591 and varians 0.1114586.
Penulis: Nur Ahmad Ricky R,
Suliyanto, Toha Saifudin
Kode Jurnal: jpmatematikadd130073
