Modeling and simultaneous hypothesis testing in nonparametric regression with mixture model of kernel and Fourier series

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The main objective in regression analysis is to estimate the regression curve. There are three approaches to estimating the regression curve, namely parametric, nonparametric and semiparametric regression approaches. In parametric regression there are many assumptions that must be met, one of which is the shape of the regression curve that must be known. Nonparametric regression analysis is recommended to be used if the pattern of the regression curve is unknown. Nonparametric regression approaches that often get the attention of researchers are Kernel, Spline, Fourier Series and Wavelet. 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. As a development of the previous research, parameter estimation was carried out for the mixed kernel nonparametric regression model and Fourier series using the Ordinary Least Square (OLS) method. Furthermore, the hypothesis testing is carried out simultaneously on the resulting estimator. Statistical inference, especially hypothesis testing, is very important because it can be used to determine whether the predictor variable has a significant effect on the model. The resulting nonparametric regression estimator model of a mixture of kernel and Fourier series is B(w, α)y. Hypothesis testing in accordance with the model is by using the F distribution approach, where F ▯ F(2 + w(q)),(n −(2 + (w)q)). Rejection area for hypothesis H0 is F > Fα,(2 + w(q)),(n − (2 + (w)q)).