A New Mixed Estimator in Nonparametric Regression for Longitudinal Data

We introduce a new method for estimating the nonparametric regression curve for longitudinal data. This method combines two estimators: truncated spline and Fourier series. This estimation is completed by minimizing the penalized weighted least squares and weighted least squares. This paper also provides the properties of the new mixed estimator, which are biased and linear in the observations. The best model is selected using the smallest value of generalized cross-validation. The performance of the new method is demonstrated by a simulation study with a variety of time points. Then, the proposed approach is applied to a stroke patient dataset. The results show that simulated data and real data yield consistent findings.

The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression

In daily life, mixed data patterns are often found, namely, those that change at a certain sub-interval or that follow a repeating pattern in a certain trend. To handle this kind of data, a mixed estimator of a Smoothing Spline and a Fourier Series has been developed. This paper describes a simulation study of the estimator in nonparametric regression and its implementation in the case of poor households. The minimum Generalized Cross Validation (GCV) was used in order to select the best model. The simulation study used generation data with a Uniform distribution and a random error with a symmetrical Normal distribution. The result of the simulation study shows that the larger the sample size n, the better the mixed estimator as a model of nonparametric regression for all variances. The smaller the variance, the better the model for all combinations of samples n. Very poor households are characterized predominantly in their consumption of carbohydrates compared to that of fat and protein. The results of this study suggest that the distribution of assistance to poor households is not the same, because in certain groups there are poor households that consume higher carbohydrates, and some households may consume higher fats.

Selection of Optimal Smoothing Parameters in Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression

In this article, we propose a new method of selecting smoothing parameters in semiparametric regression. This method is used in semiparametric regression estimation where the nonparametric component is partially approximated by multivariable Fourier Series and partly approached by multivariable Kernel. Selection of smoothing parameters using the method with Generalized Cross-Validation (GCV). To see the performance of this method, it is then applied to the data drinking water quality sourced from Regional Drinking Water Company (PDAM) Surabaya by using Fourier Series with trend and Gaussian Kernel. The results showed that this method contributed a good performance in selecting the optimal smoothing parameters.

Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Mixed estimators in nonparametric regression have been developed in models with one response. The biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. Therefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. This mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. The mixed estimator is obtained through two-stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. This estimator is also applied to the percentage of the poor population and human development index data. The results show that the proposed model can be appropriately implemented and gives satisfactory results.

The Mixed Liu Estimator in Stochastic Restricted Linear Measurement Error Model

Ghapani and Babdi [1] proposed a mixed Liu estimator in linear measurement error model with stochastic linear restrictions. In this article, we propose an alternative mixed Liu estimator in the linear measurement error model with stochastic linear restrictions. The performance of the new mixed Liu estimator over the mixed estimator, Liu estimator, and mixed Liu estimator proposed by Ghapani and Babdi [1] are discussed in the sense of mean squared error matrix. Finally, a simulation study is given to show the performance of these estimators.

MODELING EAST JAVA INDONESIA LIFE EXPECTANCY USING SEMIPARAMETRIC REGRESSION MIXED SPLINE TRUNCATED AND FOURIER SERIES

Life expectancy is one of the indicators used to evaluate the government’s performance in improving the well-being of the population. High life expectancy in an area indicates that people in the area have been assured of health and poverty has been well overcome, and vice versa. Based on national socioeconomic survey (SUSENAS) data, showing life expectancy in East Java Province from 2009 to 2013 increased by 69.15 years to 70,19 years. Although overall life expectancy in East Java province has increased, there are still some areas that have life expectancy below 65 years. This is not from the different characteristics of each religion. Therefore, the main purpose of this study is to model life expectancy in East Java using semiparametric regression with a mixed estimator of Spline Truncated and Fourier Series. Based on the research that has been done, the results that modeling the data of life expectancy using mixed estimator of Spline Truncated and Fourier Series produced a value of R2 of 99,62% which means that the predictor variables are able to explain the response variabel life expectancy of 99.62%.

Comparison of Two Estimators of the Regression Coefficient Vector Under Pitman’s Closeness Criterion

Schaffrin and Toutenburg [1] proposed a weighted mixed estimation based on the sample information and the stochastic prior information, and they also show that the weighted mixed estimator is superior to the ordinary least squares estimator under the mean squared error criterion. However, there has no paper to discuss the performance of the two estimators under the Pitman’s closeness criterion. This paper presents the comparison of the weighted mixed estimator and the ordinary least squares estimator using the Pitman’s closeness criterion. A simulation study is performed to illustrate the performance of the weighted mixed estimator and the ordinary least squares estimator under the Pitman’s closeness criterion.

Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression

So far, most of the researchers developed one type of estimator in nonparametric regression. But in reality, in daily life, data with mixed patterns were often encountered, especially data patterns which partly changed at certain subintervals, and some others followed a recurring pattern in a certain trend. The estimator method used for the data pattern was a mixed estimator method of smoothing spline and Fourier series. This regression model was approached by the component smoothing spline and Fourier series. From this process, the mixed estimator was completed using two estimation stages. The first stage was the estimation with penalized least squares (PLS), and the second stage was the estimation with least squares (LS). Those estimators were then implemented using simulated data. The simulated data were gained by generating two different functions, namely, polynomial and trigonometric functions with the size of the sample being 100. The whole process was then repeated 50 times. The experiment of the two functions was modeled using a mixture of the smoothing spline and Fourier series estimators with various smoothing and oscillation parameters. The generalized cross validation (GCV) minimum was selected as the best model. The simulation results showed that the mixed estimators gave a minimum (GCV) value of 11.98. From the minimum GCV results, it was obtained that the mean square error (MSE) was 0.71 and R2 was 99.48%. So, the results obtained indicated that the model was good for a mixture estimator of smoothing spline and Fourier series.