Estimasi Model Regresi Nonparametrik Multivariat berdasarkan Estimator Polinomial Lokal Orde Dua
Abstract: The purpose of this
Skripsi is to estimate multivariate nonparametric regression model based on second
order local polynomial estimator. Estimation of multivariate nonparametric
regression model is obtained in explicit form from function bandwidth 𝒉 and fixed point arbitrary 𝒙,
so that estimation can be done with choose optimal bandwidth which minimized
Generalized Cross Validation (GCV). Furtehermore, we explain the confidence
level (1−𝛼)100% for mean of estimation of multivariate
nonparametric regression model.
In this case, we used data of baby’s weight in 2006 at Rumah Sakit Haji
Surabaya. There are thirty observations where the response variable is weight
of baby in kilogram and predictor
variables are baby’s height in meter and head circumference of baby in meter.
The results of multivariate nonparametric regression model in data of baby’s
weight with confidence level 95% for mean of estimation baby’s weight on first
observation is 8.286≤𝐸�𝑚2,𝐻(𝑿1)�≤9.349, on second
observation is 0.673≤𝐸�𝑚2,𝐻(𝑿2)�≤12.426, then on thirty observation
is 8.538≤𝐸�𝑚2,𝐻(𝑿30)�≤9.695, with an optimal bandwidth value for 𝑋1is 1.1 and 𝑋2is
0.3. For compatibility of the result multivariate nonparametric regression is
obtained MSE = 0.992158139962808 and error random 𝜀𝑖~
𝑁(3.93603
, 1.02637).
Keywords: multivariate
nonparametric regression, second order local polynomial estimator, generalized cross
validation
Penulis: Dyah Widiantini, Suliyanto,
Eko Tjahjono
Kode Jurnal: jpmatematikadd130071
