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The statistical analysis method used to determine the effect between two or more variables is called regression analysis. The pattern of relationships between variables in regression analysis does not always have a parametric pattern. There are some cases where one or more predictor variables do not have a pattern that is called nonparametric and even has a combined pattern of parametric and nonparametric, called semiparametric. Nonparametric regression is a statistical method that is used to identify and modelling the pattern of the relationship between predictor variables and response variables whose function is unknown. One method that is widely used to estimate the regression curve using a nonparametric approach is the Fourier series. The advantage of the Fourier series is this method is quite good for describing curves whose data patterns are repeated. This study will examine the estimation of the nonparametric regression curve of the Fourier series and then modelling the Open Unemployment Rate data in Indonesia with the best model criteria based on the maximum R2 value and the minimum Generalized Cross Validation (GCV) and Mean Square Error (MSE). The results of this research shown that with the Fourier series, the minimum GCV is 2.66 with an oscillation number of 3. Then the model goodness value is 91.73% and the MSE model is 2.410. [ABSTRACT FROM AUTHOR]

Covid-19 is rapidly arising in Indonesia due to a lack of awareness of the Covid-19 dangers. It has been recorded that the sum of positive cases is 31.189 cases that happened on the 6th of July 2021. There is still an open opportunity to predict the peak of new cases and the ends of the pandemic. Many models based on various methodologies have been built for this purpose. In this article, we examine the modified Grey Model to predict the development of Covid-19 cases. Using time-series data since the pandemic happened in Indonesia, we modelized the Covid-19 cases with GM (1,1), Grey Markov, Grey Verhulst, and modification of GM (1,1) and Grey Verhults using Fourier series of error residuals methods. The result shows that the best simulation of model fitting was achieved by Grey Verhults using the Fourier series of error residuals. Furthermore, the forecasting accuracy shows that GM (1,1) show the best performance among others. We hope that the government can use this model to formulate the best policies so that the development of Covid-19 can be suppressed. [ABSTRACT FROM AUTHOR]

Nonparametric regression is one of the approaches in regression analysis to determine the relationship pattern between predictor variable and response variable. This approach can be used when the data pattern is unknown. Recently, researchers have assumed that every predictor variable in nonparametric regression has the same data pattern by using one form of the estimator for all predictor variables. However, in many cases, there are different data patterns for the relationship of each predictor variable and response variable that partially change in certain sub-intervals, some do not have a set pattern, and some others have a repeating pattern. If the estimation of each predictor variable only uses one form of an estimator, it will produce a bias estimation. Therefore, it requires a mixed estimator to get the better nonparametric regression estimation which is set with data patterns. This research evolves a mixed Spline Truncated, Kernel, and Fourier Series estimator for nonparametric regression estimation. It was applied to longitudinal data that repeatedly measured in each subject at different time intervals. A real case was presented to estimate the problem of poverty in 34 provinces in Indonesia from 2015 to 2020. Weighted Least Square (WLS) approach was utilized as method of the estimation. Based on the results of the analysis, the best nonparametric regression model was obtained, namely the model with 1 knot 1 oscillation, with the smallest GCV value of 0.25. [ABSTRACT FROM AUTHOR]

Covid-19 is an infectious disease caused by a coronavirus that was only known when the outbreak began in Wuhan, China in December 2019. All countries are infected with this outbreak so that it could impact the SDG program's goal of 2030 not being achieved, namely the target of Good Health and Wellbeing. In addition, a pandemic also affects all sectors of human life, including the national economy and health sectors. Economic growth in Indonesia has decreased by -5.32% in the second quartile of 2020. Meanwhile, in the health sector, some Covid-19 patients can only isolate independently, due to the limited number of health facilities. Therefore, it is necessary to do modeling, where the results of the analysis carried out can help to act appropriately and minimize the impact of the Covid-19 pandemic and ensure a healthy life to meet the welfare of the whole community following SDGs goals. This study uses parametric and nonparametric approaches to predict positive cases of Covid-19 in Indonesia. Modeling using a parametric approach, the ARIMA method is not suitable because it does not meet the assumptions. So that the nonparametric approach to the Fourier series estimator can be an alternative in overcoming this problem. By using a nonparametric approach, the MSE value is 12,472.11 and the determination coefficient is 98.12671%. Based on the results of the test data prediction to be compared with the actual value, the MAPE value obtained is 17.64% and this value is included in the good prediction category. [ABSTRACT FROM AUTHOR]

Regression is an analysis for determining relationship between response variables and predictor variables. There are three approaches to estimate the regression curve. Those are parametric regression, nonparametric regression, and semiparametric regression. This study focused on the estimator form of semiparametric regression curve using Fourier series approach with sine and cosine base (general); sine base; and cosine base. The best estimator, which is obtained using ordinary least square optimization was applied to model the percentage of criminal incidents in Indonesia. The goodness-of-fit criteria of a model used are high coefficient of determination, minimum Generalized Cross Validation (GCV) and Mean Square Error (MSE) value with determining parsimony model. In this study, the authors obtained the best fourier estimator for predicting percentage of criminal incidents based on cosine fourier series that had minimun GCV and MSE values, of 2.471 and of 0.0006, respectively, and determination coefficient of 77.545%. So, the estimator (cosine-fourier series) was used for predicting the out-sample data and it met Mean Absolute Error (MAE) of 0.02. [ABSTRACT FROM AUTHOR]

This paper provides a comparison between two estimators of nonparametric regression for longitudinal data, i.e., truncated spline and Fourier series. The main aim of this study is to investigate the performance of each estimator by applying the model to the pneumonia cases. Pneumonia cases in Indonesia is growing, considering the significant increase in the prevalence in just over the past ten years. The secondary data were collected from Indonesia Health Profile published by the Indonesian Ministry of Health. The predictors are the percentage of toddlers with vitamin A intake, the percentage of basic immunization coverage in infants, the percentage of poor population, and the percentage of households with proper sanitation access. Our study shows that truncated spline nonparametric regression with three-knot points and the second type weighting method is the best estimator for modeling the percentage of pneumonia cases in Java Island. [ABSTRACT FROM AUTHOR]

Shallots are one of the leading commodities that strengthen national food security. From 2013 to 2018 the development of shallots production had increased. Except in 2015 the production of shallots decreased by 0.39 percent compared to 2014. Prediction of shallots prices is needed in order to maintain price stability for supporting food security, economic stability, and trade. In predicting the price of shallots commodities, statistical modeling is carried out using parametric and nonparametric time series approaches. However, in this research the parametric approach did not meet the assumption of white noise. Therefore, the nonparametric approach of kernel estimator and Fourier series estimator was used with correlated error. Nonparametric approach is used because it has a flexible form and alternative solutions if the parametric approach does not meet the assumptions. The result was the best model to predict of shallots prices in Indonesia was modeled based on the nonparametric approaches with kernel estimator. The model met goodness criteria like the small MSE value is 757.7224 and the big determination coefficient is 99.95%. The goodness criteria for kernel estimator is better than Fourier series estimator. The kernel estimator has good performance to predict the price of shallots with small MAPE value is 1.088%. [ABSTRACT FROM AUTHOR]

In statistical modeling, Fourier series estimator is frequently applied to time series data in nonparametric approach. Based on nonparametric regression study, Fourier series estimator has good flexibility to predict seasonal and the combination of trend and seasonal data pattern. This paper proposes an application of Fourier series estimator in biostatistics and epidemiology cases. One of the important problems in health science is disease prevention efforts. For prevention efforts, prediction the number of sufferers is determined. Fourier series estimator is applied to predict the number of sufferers for seasonal diseases like dengue fever and malaria that becomes a main issue in Indonesia. We used secondary data from the Ministry of Health of Indonesia to model and predict the number of dengue fever and malaria sufferer in Indonesia based on Fourier series estimator. A selected model that be chosen has met the goodness of model's criteria such as the small Generalized Cross Validation (GCV), Mean Square Error (MSE), and the large determination coefficient. The selected model also considered the model parsimony. Therefore, Fourier series estimator was able to predict the number of sufferers for seasonal diseases and the prediction produced small value of Mean Absolute Percentage Error (MAPE) and MSE. Thus, the result can be used to give recommendation to related policy maker. [ABSTRACT FROM AUTHOR]