INTERVAL ESTIMATION OF NONPARAMETRIC REGRESSION CURVE FOURIER SERIES (Case Study Data of Poverty in East Java Province 2021) Idrus Syahzaqi (a*), Jerry Dwi Trijoyo Purnomo (a), I Nyoman Budiantara (a)
a) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia
* idrus.syahzaqi[at]gmail.com
Abstract
Regression is one of the analytical methods used to determine the relationship pattern between response variables and predictor variables. There are three approaches used in regression, namely parametric, nonparametric, and semiparametric regression. When the data used is not known the shape of the regression curve, then the nonparametric regression approach can be an option. In addition, the nature of flexibility in nonparametric regression can be seen by setting certain criteria, for example the presence of optimal oscillations in the nonparametric Fourier series regression, then the data will determine the shape of the estimation of the regression curve, without being influenced by the subjectivity factor of the researcher. Research using nonparametric regression has been carried out a lot. However, from several studies that have been conducted, there are still not many studies that examine interval estimation in the nonparametric regression estimator of the Fourier Series. The interval estimation for the nonparametric regression curve of the Fourier series estimator has the advantage of having a smaller error probability value than point estimation because it is not focused on one point but is based on a range of the highest (max) and lowest (min) values. The application of interval estimation can be applied to various fields of science, including in the field of economics in the case of poverty. East Java Province was chosen as the object of research, considering that this region occupies the first position with the highest poverty rate in Indonesia. This research aims to estimate the nonparametric Fourier series regression interval that is applied to the percentage of poverty in East Java Province. The function used in the nonparametric regression estimator of the Fourier Series is the cos function. The method used to determine the optimum number of oscillation parameters in the Fourier Series uses the minimum Generalized Cross Validation (GCV) value.
Keywords: Interval Estimation, Nonparametric Regression, Fourier Series, Percentage of Poverty
