The pattern in a relationship between the response variable and the predictor variable can be known and some cannot be known. In determining the unknown pattern of relationships, nonparametric regression approaches can be used. The nonparametric regression approach is very flexible. One of the most frequently used nonparametric regression approaches is the truncated spline. Truncated splines are polynomial pieces that are segmented and continuous. The purpose of this study is to obtain the best estimator model in the Gini Ratio case against the variables suspected of influencing it, then perform simultaneous hypothesis testing on the nonparametric regression model. The criteria for the goodness of the model use the GCV and R2 values. In the case modeling of the District / City Gini Ratio in East Java Province using a nonparametric regression approach, it was found that the truncated spline estimator with 3 knots points gave quite good results. This is indicated by the coefficient of determination of the truncated spline estimator, which is 84.76%. Based on the results of simultaneous testing, it was found that the open unemployment rate, the percentage of poor people and the rate of economic growth simultaneously had an influence on the Gini Ratio.
ABSTRAKPendekatan regresi nonparametrik digunakan apabila hubungan antara variabel prediktor dan variabel respon tidak diketahui polanya. Spline truncated dan deret Fourier merupakan estimator dalam pendekatan nonparametrik yang terkenal, karena memiliki fleksibilitas yang tinggi dan mampu menyesuaikan terhadap sifat lokal data secara efektif. Penelitian ini bertujuan untuk mendapatkan estimator model regresi nonparametrik terbaik menggunakan spline truncated dan deret Fourier. Metode estimasi kurva regresi nonparametrik dilakukan dengan menyelesaikan optimasi Ordinary Least Squares (OLS). Kriteria kebaikan model menggunakan GCV, R2 dan MSE. Pemodelan regresi nonparametrik diterapkan pada data Case Fatality Rate (CFR) akibat Demam Berdarah Dengue (DBD) di Indonesia. Berdasarkan hasil analisis, hasil estimasi dari pemodelan regresi nonparametrik menunjukkan bahwa estimator spline truncated memberikan performa yang lebih baik dibandingkan estimator deret Fourier. Hal ini ditunjukkan dengan nilai R2 dari estimator spline truncated yaitu sebesar 91,80% dan MSE sebesar 0,04, sedangkan dengan estimator deret Fourier diperoleh nilai R2 sebesar 65,44% dan MSE sebesar 0,19.ABSTRACTThe nonparametric regression approach is used when the relationship between the predictor variable and the response variable is unknown. Spline truncated and Fourier series are well-known estimators in the nonparametric approach because they have high flexibility and are able to adjust to the local properties of the data effectively. This study aims to obtain the best nonparametric regression model estimator using the truncated spline and the Fourier series. The nonparametric regression curve estimation method is done by completing the Ordinary Least Squares (OLS) optimization. The criteria for the goodness of the model use GCV, R2, and MSE. Nonparametric regression modeling is applied to Case Fatality Rate (CFR) modeling due to Dengue Hemorrhagic Fever (DBD) in Indonesia. Based on the analysis, the estimation results from the nonparametric regression modeling show that the truncated spline estimator provides better performance than the Fourier series estimator. This is shown by the R2 value of the truncated spline estimator which is 91.80% and the MSE is 0.04, while the Fourier series estimator obtained an R2 value of 65.44% and MSE of 0.19.
The pattern of the relationship between the response variable and the unknown predictor can be determined using a nonparametric regression approach. Nonparametric regression allows it to be used for response variables following different curves between one variable and another. In this regression, there are several types of approaches including the kernel, spline, and Fourier series. In its use, there is not only one type of approach, but can be in the form of a mixture, such as a mixture of a spline and Fourier series, a kernel and a Fourier series, and so on. In this study, in modeling the HDI cases in East Java Province, nonparametric regression mixed kernels, Spline Truncated, and Fourier series were used. The results of research that have been applied to HDI in East Java with the predictor variables for APM SMA, Morbidity, and GRDP per Capita are using the mixed kernel, Spline Truncated, and Fourier series nonparametric regression approach with three-knot points and three oscillations. Good because the coefficient of determination of the estimator is 75.1041%.
Currently the world is facing a global problem in the form of the COVID-19 pandemic. The spread of the COVID-19 outbreak continues to move significantly, especially in Indonesia. Since it was announced by President Joko Widodo in early March until now, the number of positive cases of COVID-19 has reached 418.375 cases. The impact of COVID-19 is a serious threat to the global economy. COVID-19 attacks the movement of stocks on global exchanges. The Composite Stock Price Index (IHSG) has touched its lowest level in history due to COVID-19. COVID-19 can be considered as an event that occurs out of control, so of course it will affect various sectors, particularly the economic sector, by spreading fear for investors and creating uncertainty in the global economy. The purpose of this study is to determine the impact of COVID-19 on the IHSG and to build a model that can be used for forecasting. The analytical method used is intervention analysis. The intervention model is used to model data that contains shocks. In this case, the suspected shock is the COVID-19. The intervention function used is the step function. Furthermore, risk measurement will be carried out so that risk is at a controllable level. Measurable risk can reduce the chance of loss that may be borne by investors. The method used is Value at Risk (VaR). The risk measurement is applied to the outcome forecasting data from the intervention model. Based on the results analysis, intervention model shows that COVID-19 has had an impact and a harsh slap on IHSG. Forecasting results from the intervention model have a good accuracy, with MAPE from in-sample is 0,76%. Then the forecasting results from the intervention model have a Value at Risk (VaR) which ranges from 0,45% to 1,96% with a confidence level of 95%.
Regression modeling with a semiparametric approach is a combination of two approaches, namely the parametric regression approach and the nonparametric regression approach. The semiparametric regression model can be used if the response variable has a known relationship pattern with one or more of the predictor variables used, but with the other predictor variables the relationship pattern cannot be known with certainty. The purpose of this research is to examine the estimation form of the semiparametric spline truncated regression model. Suppose that random error is assumed to be independent, identical, and normally distributed with zero mean and variance , then using this assumption, we can estimate the semiparametric spline truncated regression model using the Maximum Likelihood Estimation (MLE) method. Based on the results, the estimation results of the semiparametric spline truncated regression model were obtained p=(inv(M'M)) M'y
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