Optimal Knots Point and Bandwidth Selection in Modeling Mixed Estimator Nonparametric Regression

Stocks are securities that can be bought or sold by individuals or institutions as a sign of participating or possessing a company in the amount of its proportions. From the lens of market capitalization values, stocks are divided into 3 groups: large capitalization (Big-Cap), medium capitalization (Mid-Cap) and small capitalization (Small-Cap). Longitudinal data is observation which is conducted as n subjects that are independent to each subject observed repeatedly in different periods dependently. Smoothing technique used to estimate the nonparametric regression model in longitudinal data is local polynomial estimator. Local polynomial estimator can be obtained by WLS (Weighted Least Square) methods. Local polynomial estimator is very dependent on optimal bandwidth. Determination of the optimal bandwidth can be obtained by using GCV (Generalized Cross Validation) method. Among the Gaussian kernel, Triangle kernel, Epanechnikov kernel and Biweight kernel, it is obtained the best model using Gaussian kernel. Based on the application of the model simultaneously, it is obtained coefficient of determination of 97,80174% and MSE values of 0,03053464. Using Gaussian kernel, MAPE out sample of data is obtained as 11,74493%. Keywords: Longitudinal Data, Local Polynomial, Stocks

Nonparametric regression is a statistical technique employed to discern the relationship pattern between a predictor variable and a response variable in the absence of prior information about the form of the regression function or when the pattern of the regression curve is unknown. Truncated spline nonparametric regression represents an approach for aligning data, considering the curve's smoothness. It possesses continuous segmented characteristics, offering flexibility and adeptly accommodating the explanation of local data function features. The study aims to identify the influencing factors on the open unemployment rate in Kalimantan Island during 2020. Additionally, it seeks to derive a spline truncated nonparametric regression model for Open Unemployment Rate data in Kalimantan Island for the same year. The study employs a nonparametric regression model with a spline truncated method, determining optimal knot points based on the minimum Generalized Cross Validation (GCV) value. The study reveals that the most effective spline truncated nonparametric regression model features two knot points. Significant factors influencing the open unemployment rate include the labor force participation rate, school year expectations, regional gross domestic product at current prices, and the human development index.

Nonparametric regression is a regression approach that is used to determine the relationship between the response variable and the predictor variable if the shape of the regression curve is unknown. One of the popular estimators used in nonparametric regression is the Fourier series estimator. Fourier series nonparametric regression is generally used when the pattern of the investigated data is unknown and there is a tendency for the pattern to repeat. The purpose of this study is to estimate nonparametric regression using the Fourier series approach and to find out the factors that influence the open unemployment rate on the island of Borneo in 2021. The criteria for the goodness of the model used Generalized Cross Validation (GCV) and the coefficient of determination ( ). Based on the results, it was found that the best nonparametric regression model for the Fourier series was the model with 5 oscillations which indicated a minimum GCV of 10.47 and an of 74.22%. Furthermore, based on the results of parameter significance testing either simultaneously or partially, it shows that all predictor variables have a significant effect on the open unemployment rate. The predictor variables include the labor force participation rate, the average length of schooling, the percentage of poor people, economic growth rate, and total population.

There are three nonparametric regression approaches, namely, parametric, nonparametric and semi-parametric regression. Nonparametric regression allows the response variable to follow a different curve from one predictor variable to another. In paired data, the components of predictor variable and the response variable are assumed to follow unknown data patterns, so that they can be approximated by a kernel based regression model and Fourier series. The base components are approximated by kernel functions and Fourier series functions. Error is assumed to be normally distributed with zero mean and constant variance. The aim of this research is to make a kernel-based nonparametric regression model and Fourier series on poverty data in the Province of Bali. The research phase method begins with the introduction of the kernel based nonparametric regression model and the Fourier series. The next step is to study the estimation of the regression curve. The function estimation results are highly dependent on the bandwidth, smoothing and oscillation parameters. The resulting model gives a value of R2=0.6278, means that the used variables can explain the model by 62.78 percent. From the obtained modeling re-sults, the Open Unemployment Rate has a positive effect on the percentage of poor people in Bali. Keywords: Nonparametric Regression; Modeling; Kernel; Fourier Series.

Background: Nowadays, forecasting models based on nonparametric models have been developed in many branches of science such as mathematics and economics. However, the relatively complicated structure of these models has made them less practical in medical sciences. Objectives: In this study, we investigated the application of a nonparametric regression model to predict the psychological symptoms appearing six months after mild traumatic brain injury. We also made a comparison between the performance of nonparametric regression and artificial neural network models in predicting the psychological symptoms. Methods: In a six-month period during 2015 - 2017, information of 100 mild traumatic patients was included in a prospective cohort study. The data were then divided randomly into two groups of training (n = 50) and testing (n = 50) for 100 times. In the training group, the focus was on 100 artificial neural network and nonparametric regression models. However, in the testing group, a comparison was made between the values obtained using the two final models. To compare the models, the ROC curve and the accuracy rate were finally applied. Results: According to the obtained results, the nonparametric regression model showed an accuracy rate of 91.25% while the neural network model had an accuracy rate of 85.34%. In the experimental set for both neural network and nonparametric regression models, the area under the ROC curve appeared to be 81.51% and 85.73 %, respectively. Conclusions: The nonparametric regression model appeared to be more powerful than the neural network model in predicting psychological symptoms.

Researchers use the nonparametric regression method because it provides excellent flexibility in the modeling process. Nonparametric regression procedures can be used if the relationship pattern between the predictor and response variables is unknown. The truncated spline method is one of the most frequently used nonparametric regression methods. A truncated spline is a polynomial slice with continuous segmented properties, and the resulting curve is relatively smooth. The advantage of truncated splines is that they can be used on data that experience behavior changes at specific intervals. The nonparametric spline truncated bi-response regression approach is used when one or more predictor variables affect the two response variables with the assumption that there is a correlation between the response variables. This study aimed to obtain the best spline truncated bi-response nonparametric regression model on life expectancy data and the prevalence of underweight children in Indonesia in 2021. The data used comes from the Central Bureau of Statistics and the Indonesian Ministry of Health. The optimal knot point selection method uses the Generalized Cross Validation (GCV) method. The results showed that the best model formed was obtained using three-knot points based on a minimum GCV value of 22.77 and a coefficient of determination of 99.58%.

In many applications two or more dependent variables are observed at several values of the independent variables, such as at time points. The statistical problems are to estimate functions that model their dependences on the independent variables, and to investigate relationships between these functions. Nonparametric regression model, especially smoothing splines provides powerful tools to model the functions which draw association of these variables. Penalized weighted least-squares is used to jointly estimate nonparametric functions from contemporaneously correlated data. In this paper we formulate the multi-response nonparametric regression model and give a theoretical method for both obtaining distribution of the response and estimating the nonparametric function in the model. We also estimate the smoothing parameters, the weighting parameters and the correlation parameter simultaneously by applying three methods: generalized maximum likelihood (GML), generalized cross validation (GCV) and leaving-out-one-pair cross validation (CV).

Poverty is a complex problem that has an impact on various social problems such as education, unemployment, health and economic growth. Therefore, the problem of poverty is important to overcome in order to create population welfare. One of the analyses that can be used to model the percentage of poverty is regression analysis. Regression analysis is divided into two approaches, namely parametric and nonparametric. Parametric regression has several assumptions while, the only assumption nonparametric regression shape of the curve does not form a certain pattern. There are several approaches to nonparametric regression, one of which is the Fourier Series. The purpose of this study is to model the percentage of poverty in West Sumatra Province. The unclear shape of the curve in the data used is a consideration for using nonparametric regression. Then it is known that the data used in this study is data per region which tends to have a fluctuating nature. So it is suitable to use the Fourier series approach. In this research, nonparametric regression modeling with one, two, and three oscillation parameters was attempted. The best model was obtained which consisted of two oscillation parameters with a Generalized Cross Validation (GCV) value of 2.110 and R² of 92.44%.

Nonparametric regression is a model approach method that is used when the shape of the regression curve between the response variable and the predictor variable is assumed to have an unknown shape or pattern. One of the estimators in the nonparametric regression approach is the truncated spline which has the ability to handle data whose behavior changes at certain sub intervals. The purpose of this study was to obtain the estimated value of the parameters of the nonparametric regression model with a truncated spline approach at one knot point, two knot points, and three knot points for kick height data of yeop chagi taekwondo athletes in Samarinda City. The results showed that the truncated spline nonparametric regression model was the best in modeling high kick height data for yeop chagi taekwondo athletes in Samarinda City with three knot points. This model has the minimum Generalized Cross Validation (GCV) value of 7.94 with an R2 value of 94.72% and a Mean Square Error (MSE) value of 2.62. Based on the results of the model parameter significance test, it was concluded that the factors that influence the kick height of the yeop chagi taekwondo athlete in Samarinda City are flexibility, leg power, leg length, and waist circumference.

In major domestic cities, the development of urban expressway is network oriented. The traffic flow forecasting system is the important prerequisite and foundation for realizing real-time traffic management and control. However, the traffic flow forecasting research is mainly based on highways. Research and application of short-term traffic forecasting for urban expressway is severely insufficient. Therefore, the study of urban expressway flow forecasting is discussed and a short-term traffic flow forecasting system for urban expressway based on k-NN nonparametric regression model is proposed in this study. First, the study analyzes the characteristics and needs of the urban expressway traffic flow, introduces the k-NN nonparametric regression model, and designs the short-term traffic flow forecasting system based on k-NN overall. Then, the short-term urban expressway flow forecasting system based on k-NN is established in three aspects: the historical database, the search mechanism and algorithm parameters, and the forecasting plan. Finally, a short-term traffic forecasting for urban expressway based on k-NN nonparametric regression model is developed in the VS2010 VC++ platform. Utilizing the Shanghai urban expressway section measured traffic flow data, the comparison of average and weighted k-NN nonparametric regression model is discussed and the reliability of the forecasting result is analyzed. Results show that the accuracy of the proposed method, under the five-minute interval, is over 90%, which best proves the reasonableness of the proposed forecasting model based on the k-NN nonparametric model.

Nonparametric regression modelling for data applies the relationship between predictor and response variables without considering any particular trend. The main principle of nonparametric regression is estimating an unknown smooth function. Local polynomial regression is one of several methods for estimating smooth functions used in nonparametric regression models. There are two parameters in the local polynomial regression model the smoothing parameter and the polynomial degree parameter. Generalized Cross Validation is a classical method used to determine optimal smoothing parameter in nonparametric regression. The smoothing parameter that gives the minimum value of Generalized Cross-Validation is the optimal parameter. We apply the optimal smoothing parameter for local polynomial regression modelling using data on the regional domestic product growth rate of the business field in North Sumatra Province. The simulation results show a polynomial of degree two is better than degree one. Investigation of the effects of the Covid-19 pandemic shows that the predicted growth rate is far from the expected growth.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Helida Nurcahayani, I. Nyoman Budiantara, Ismaini Zain; The curve estimation of bi-response nonparametric regression using truncated spline on East Java SDGs achievement. AIP Conference Proceedings 25 January 2023; 2554 (1): 030007. https://doi.org/10.1063/5.0106527 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

The nonparametric binary logistic model assumes that the logit function is a linear function in the parameter, where the parameter depends on arbitrary fixed point. This study discusses the estimation of a nonparametric binary logistic regression model using the local likelihood logit estimation method. This method assumes that the log likelihood logit function depends on the multivariate kernel weighting. The parameter estimation of a nonparametric binary logistic regression model is obtained by maximizing the log likelihood logit function. The parameter estimation result are implicit, so to estimate it started with determining the optimal bandwidth value based on the maximum Cross Validation value. Furthermore, the optimal bandwidth value is used to estimate parameters using the multivariate Newton-Raphson algorithm until converging iterations are obtained. The parameter estimation process is done by creating a program in OSS-R software. This study also discusses the application of parametric and nonparametric binary logistic regression models in the case study of Type II Diabetes Mellitus patients at the Surabaya Hajj General Hospital. The modeling results show that the classification accuracy value of the parametric and nonparametric binary logistic regression models is 80.2% and 100% for the cut of value of 0.5.

Semarang is the provincial capital of Central Java, with infrastructure and economic’s growth was high. The phenomenon of power outages that occurred in Semarang, certainly disrupted economic development in Semarang. Large electrical energy consumed by industrial-scale consumers and households in the San Francisco area, monitored or recorded automatically and presented into a historical data load power consumption. Therefore, this study modeling the load power consumption at a time when not influenced by the use of electrical load (t-1)-th. Modeling using nonparametric regression approach with Local polynomial. In this study, the kernel used is a Gaussian kernel. In local polynomial modeling, determined optimum bandwidth. One of the optimum bandwidth determination using the Generalized Cross Validation (GCV). GCV values obtained amounted to 1425.726 with a minimum bandwidth of 394. Modelling generate local polynomial of order 2 with MSE value of 1408.672. Keywords: electrical load, local polinomial, gaussian kernel, GCV.

This chapter reviews the literature on variable selection in nonparametric and semiparametric regression models via shrinkage. We highlight recent developments on simultaneous variable selection and estimation through the methods of least absolute shrinkage and selection operator (Lasso), smoothly clipped absolute deviation (SCAD), or their variants, but restrict our attention to nonparametric and semiparametric regression models. In particular, we consider variable selection in additive models, partially linear models, functional/varying coefficient models, single index models, general nonparametric regression models, and semiparametric/nonparametric quantile regression models.