Modeling and Simultaneous Hypothesis Testing in Nonparametric Regression with mixture model of Kernel and Fourier Series Andy Rezky Pratama Syam (a*), Vita Ratnasari (a), I Nyoman Budiantara (a)
a) Department of Statistics: Faculty of Science and Data Analysis, Institut Teknologi Sepuluh Nopember, Jl. Arief Rahman Hakim, Surabaya, 60111, Indonesia
*andyrezkypratama[at]gmail.com
Abstract
The main objective in regression analysis is to estimate the regression curve. There are three approaches to estimating the regression curve, namely the parametric, nonparametric and semiparametric regression approaches. In parametric regression there are many assumptions that must be met, one of which is the form of the regression curve that must be known. If the pattern of the regression curve is unknown, then nonparametric regression analysis is recommended to be used. Nonparametric regression approaches that often get the attention of researchers are Kernel, Spline, Fourier Series and Wavelets. In its application, not all predictor variables have the same data pattern, so a mixed estimator is needed to solve the problem of differences in data patterns between predictor variables. Among several nonparametric approaches, regression with the kernel approach and the Fourier series have been widely used to solve problems in research. As a development of previous research, parameter estimation was carried out for the nonparametric regression model of the mixture of kernels and the Fourier series using the Ordinary Least Square (OLS) method. Furthermore, simultaneous hypothesis testing is carried out on the resulting estimators. Statistical inference, especially hypothesis testing, is very important because it can be used to determine whether the predictor variables have a significant effect on the model. The test statistics used in the simultaneous hypothesis testing in the nonparametric regression of the kernel mixture and the Fourier series were obtained using the Likelihood Ratio Test (LRT) method
