Nonparametric Regression Curves Research Articles

Prediction of seawater salinity based on comparison of truncated spline estimators, Fourier Series and Kernel

Salinity is one of the factors that affect salt production. Salinity is defined as the level of saltiness or too much salt in water. The salt in question is a variety of ions dissolved in water, including table salt (NaCl). The higher the level of NaCl contained, the better the quality of the salt formed. This low quality causes Indonesia to import salt, both consumption salt and industrial salt. Because most of the quality of salt still does not meet the criteria of SNI. For this reason, it is necessary to predict the salinity of seawater to help determine the next steps or policies in improving the quality of salt in Indonesia, especially in the Madura area. This research is examined in the form of a nonparametric regression curve estimator with a truncated spline estimator approach, Fourier series and kernel. From the comparison results, the best model for predicting seawater salinity is the estimator of the Fourier series base sine cosine with an oscillation parameter (k) of 2 with a GCV value of 5.017987 and MSE and a coefficient of determination of 0.06299933 and 94.64373%. So the prediction results obtained in this study are close to accurate with MAPE values of 0.07225208%, MSE of 0.0001441417 and coefficient of determination of 99.99%.

Quantifying Trends of Historical Climatic Variables in the Jessore Region of Bangladesh

The aim of the study was to detect trends in salient key climate variables in the Jessore region of Bangladesh for the years 1985–2014, and the data was collected from the Bangladesh Meteorological Department (BMD). Annual rainfall, annual maximum temperature, and annual cloud coverage were analyzed using the non-parametric Mann-Kendall test, linear regression, and LOWESS curve to detect trends in the series. The rainfall and cloud coverage showed a decline trend at a rate of (4.50 mm/year; 45.02 mm/decade) and (0.045 octas/year; 0.45829 oktas/decade), respectively, whereas temperature manifested an increment trend (0.0285°C/year; 0.2854°C/decade), where cloud coverage was the only significant variable. The structural breakdown point was found using the graphical method and the Chow test, which showed in 2004 that both the series containing breakdown points and cloud coverage exhibit statistical significance.

Modeling the Hotel Tax Revenue in Central Lombok using Nonparametric Regression

In Central Lombok Regency, the hotel tax is one of the highest incomes contributing to Regional Original Revenue. A hotel tax is a tax on services provided by the hotel. This research aims to estimate the nonparametric kernel regression curve on hotel tax revenue data in Central Lombok. The method used is nonparametric kernel regression analysis with the seven kernel functions. The results of the analysis with the Generalized Cross Validation (GCV) criteria, the optimal bandwidth values ​​generated by the seven kernel functions have varying values. Although the bandwidth values ​​vary, the resulting estimation results are similar, and the comparison of the Mean Square Error (MSE) values ​​of the seven kernel functions is not significantly different.

A Truncated Spline and Local Linear Mixed Estimator in Nonparametric Regression for Longitudinal Data and Its Application

Longitudinal data modeling is widely carried out using parametric methods. However, when the parametric model is misspecified, the obtained estimator might be severely biased and lead to erroneous conclusions. In this study, we propose a new estimation method for longitudinal data modeling using a mixed estimator in nonparametric regression. The objective of this study was to estimate the nonparametric regression curve for longitudinal data using two combined estimators: truncated spline and local linear. The weighted least square method with a two-stage estimation procedure was used to obtain the regression curve estimation of the proposed model. To account for within-subject correlations in the longitudinal data, a symmetric weight matrix was given in the regression curve estimation. The best model was determined by minimizing the generalized cross-validation value. Furthermore, an application to a longitudinal dataset of the poverty gap index in Bengkulu Province, Indonesia, was conducted to illustrate the performance of the proposed mixed estimator. Compared to the single estimator, the truncated spline and local linear mixed estimator had better performance in longitudinal data modeling based on the GCV value. Additionally, the empirical results of the best model indicated that the proposed model could explain the data variation exceptionally well.

CURVE ESTIMATION AND ESTIMATOR PROPERTIES OF THE NONPARAMETRIC REGRESSION TRUNCATED SPLINE WITH A MATRIX APPROACH

Regression analysis is one of the statistical analyses used to estimate the relationship between the predictor and the response variable. Data are given in pairs, and the relationship between the predictor and the response variable was assumed to follow a nonparametric regression model. This model is flexible in estimating the curve when a typical data pattern does not follow a specific pattern. The nonparametric regression curve was approached by using the truncated spline function with several knots. The truncated spline estimator in nonparametric regression is linear in the observation. It is highly dependent on the knot points. The regression model's random error is assumed to have an independent normal distribution with zero mean and equal variance. The truncated spline's curve estimate was obtained by minimizing the error model through the least squared optimization method. The nonparametric regression truncated spline's estimator properties are linear, unbiased, and if the error is normally distributed, the estimator is normally distributed.

A method for determining groups in nonparametric regression curves: Application to prefrontal cortex neural activity analysis.

Generalized additive models provide a flexible and easily-interpretable method for uncovering a nonlinear relationship between response and covariates. In many situations, the effect of a continuous covariate on the response varies across groups defined by the levels of a categorical variable. When confronted with a considerable number of groups defined by the levels of the categorical variable and a factor-by-curve interaction is detected in the model, it then becomes important to compare these regression curves. When the null hypothesis of equality of curves is rejected, leading to the clear conclusion that at least one curve is different, we may assume that individuals can be grouped into a number of classes whose members all share the same regression function. We propose a method that allows determining such groups with an automatic selection of their number by means of bootstrapping. The validity and behavior of the proposed method were evaluated through simulation studies. The applicability of the proposed method is illustrated using real data from an experimental study in neurology.

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.

An Analysis about Fourier Series Estimator in Nonparametric Regression for Longitudinal Data

Fourier series is a function that is often used Mathematically and Statistically especially for modeling. Here, Fourier series can be constructed as an estimator in nonparametric regression. Nonparametric regression is not only using cross section data, but also longitudinal data. Some of nonparametric regression estimators have been developed for longitudinal data case, such as kernel, and spline. In this study, we concentrate to develop an inference analysis that related to Fourier series estimator in nonparametric regression for longitudinal data. Nonparametric regression based on Fourier series is capable to model data relationship with fluctuation or oscillation pattern that represents with sine and cosine functions. For point estimation analysis, Penalized Weighted Least Square (PWLS) is used to determine an estimator for parameter vector in nonparametric regression. Different with previous studies, PWLS is used to get smooth estimator. The result is an estimator for nonparametric regression curve for longitudinal data based on Fourier series approach. In addition, this study also investigated the asymptotic properties of the nonparametric regression curve estimators using the Fourier series approach for longitudinal data, especially linearity and consistency. Some study cases based on previous research and a new study case is given to make sure that Fourier series estimator in nonparametric regression has good performance in longitudinal data modeling. This study is important in order to develop further inferences Statistics, such as interval estimation and test hypothesis that related nonparametric regression with Fourier series estimator for longitudinal data.

Kernel multivariable semiparametric regression model in estimating the level of open unemption in East Java Province

Semiparametric regression is a combination of parametric regression and nonparametric regression. Parametric regression curve components are approximated by multivariable linear functions, nonparametric regression curve components are approximated by Gaussian Kernel function. The purpose of this study is to obtain an estimate of the shape in semiparametric regression using the Kernel estimator and to model the Open Unemployment Rate (TPT) in East Java Province using the semiparametric regression model. This semiparametric regression model estimates on bandwidth. Semiparametric regression model is obtained by minimizing the Generalized Cross Validation function. The semiparametric regression model used to model TPT case data in East Java Province.

Spline and Kernel Mixed Nonparametric Regression for Malnourished Children Model in West Nusa Tenggara

Health sector development is essential to improve human life quality, especially in West Nusa Tenggara (NTB) Province. Based on data from the NTB Provincial Health Office from 2011 to 2016, children under five suffering from malnutrition continued to increase, caused by several factors that affected the incident. Therefore, appropriate analysis is needed to model children who suffer from malnutrition in NTB Province in 2016, consisting of 10 districts based on the variables that influence it. The analysis in this study was carried out using a nonparametric regression mixed-model spline truncated and kernel. The estimation of the nonparametric regression curve depends on the optimal knot points and bandwidths parameter. Therefore, in determining the optimal knot points and bandwidths obtained from Generalized Cross-Validation (GCV). Based on the analysis that has been done, we obtained a nonparametric regression mixed-model spline truncated and kernel optimal knot points, such as for each variable and optimum bandwidths, such as and , with the value of GCV. The mixed model acquired has a good model by considering the values of and MSE. Besides, the MAPE value indicated a high degree of accuracy, so that the model obtained has an excellent forecast.

Mixed Truncated Spline and Kernel Nonparametric Regression Model on Population Growth Rate in West Nusa Tenggara Province

This study was conducted by considering the data pattern that differs from each independent variable to the dependent variable. If only one estimator is used to estimate the nonparametric regression curve, the resulting estimator does not match the data pattern, less precise, and tends to produce large errors. Therefore, this study aimed to model the mixed truncated spline and kernel nonparametric regression on data and predict the population growth rate in West Nusa Tenggara Province by considering the Mean Absolute Percentage Error (MAPE). Based on the study conducted, relationships generated by x 1,x 2, x 7, x 8 formed specific patterns and were indicated to follow the spline approach’s characteristics. In contrast, the pattern generated by x 3, x 4, x 5, x 6, x 9 showed the data distribution with no specific pattern and were addressed to follow the kernel approach’s characteristics. The best model was obtained with the optimal bandwidth for each variable and 3 points of optimal knots. The mixed truncated spline and kernel nonparametric regression model was suitable for modeling and predicting population growth rate data in West Nusa Tenggara Province with a relatively high proportion and a high degree of accuracy.

Van Hiele Theory-Based Instruction and Grade 11 Students’ Geometric Proof Competencies

South African matric results on the National Senior Certificate indicate low success in geometry, as do other African countries such as Nigeria. This poor performance affects potential career choices for students and limits the number of students who enter the highly-needed engineering fields on the African continent. Hence, this paper reports findings from a quasi-experiment involving 186 Grade 11 students from four conveniently selected township secondary schools in the Limpopo province of South Africa. The study tested the effect of Van Hiele theory-based instruction on the students’ geometric proof competencies. Data were collected using a geometry proof test and analysed using nonparametric analysis of covariance. Results showed that there was a statistically significant difference in students’ performance between the treatment and control groups (𝑇=595.9,𝑝=.005,𝜂𝑝2 =.684). Analysis of nonparametric regression curves fitted for the treatment and control groups showed that the treatment group had higher post-test scores than the control group. It was therefore concluded that Van Hiele theory-based instruction is more effective in teaching non-routine geometric proofs than conventional instruction. The study recommends that geometry teachers in upper secondary school should consider implementing Van Hiele theory-based instruction to enhance students’ geometric proof competence.

Test Efficiency Analysis of Parametric, Nonparametric, Semiparametric Regression in Spatial Data

Regression analysis has three approaches in estimating the regression curve, namely: parametric, nonparametric, and semiparametric approaches. Several studies have discussed modeling with the three approaches in cross-section data, where observations are assumed to be independent of each other. In this study, we propose a new method for estimating parametric, nonparametric, and semiparametric regression curves in spatial data. Spatial data states that at each point of observation has coordinates that indicate the position of the observation, so between observations are assumed to have different variations. The model developed in this research is to accommodate the influence of predictor variables on the response variable globally for all observations, as well as adding coordinates at each observation point locally. Based on the value of Mean Square Error (MSE) as the best model selection criteria, the results are obtained that modeling with a nonparametric approach produces the smallest MSE value. So this application data is more precise if it is modeled by the nonparametric truncated spline approach. There are eight possible models formed in this research, and the nonparametric model is better than the parametric model, because the MSE value in the nonparametric model is smaller. As for the semiparametric regression model that is formed, it is obtained that the variable X2 is a parametric component while X1 and X3 are the nonparametric components (Model 2). The regression curve estimation model with a nonparametric approach tends to be more efficient than Model 2 because the linearity assumption test results show that the relationship of all the predictor variables to the response variable shows a non-linear relationship. So in this study, spatial data that has a non-linear relationship between predictor variables and responses tends to be better modeled with a nonparametric approach.

Estimation of Matrix Variance-Covariance on Nonparametric Regression Spline Truncated for Longitudinal Data

Regression analysis is a statistical analysis used to determine the pattern of relationships between predictor variables and response variables. There are two models estimation approaches in regression analysis, namely parametric regression and nonparametric regression. The parametric regression approach is used if the shape of the regression curve is known. In cases with unknown relationship patterns, the development is done using nonparametric regression. Nonparametric regression is a model estimation method which is based on an approach that is not bound by certain assumptions of the regression curve shape. One of the most commonly used nonparametric regression curve estimates is the spline approach. Spline is one of the nonparametric approaches that is often used and has a very good ability to handle data characters that are smooth as well as data whose behavior changes at certain sub-intervals. Theoretically, the spline approach is not only able to estimate nonparametric regression curves for cross section data, but can also be developed for longitudinal data. Longitudinal data is a combination of cross section data and time series data where the longitudinal data between subjects are mutually independent, but between observations are dependent. This study aims to find the estimation curves of spline truncated multivariable nonparametric regression for longitudinal data using the Weighted Least Square (WLS) method and to find the estimation of variance-covariance matrix using the Maximum Likelihood Estimate (MLE) method.

Comparing two nonparametric regression curves in the presence of long memory in covariates and errors

This paper discusses the problem of testing the equality of two nonparametric regression functions against two-sided alternatives in the presence of long memory in the common covariate and errors. The proposed test is based on a marked empirical process of the differences between the response variables. We discuss asymptotic null distribution of this process and consistency of the test for a class of general alternatives. We also conduct a Monte Carlo simulation study to evaluate the finite sample level and power behavior of the test at some alternatives.

Testing Critical Points of Non-Parametric Regression Curves: Application to the Management of Stalked Barnacles

Summary Several aquatic living resources are overexploited. An example of this is a barnacle fishery, which is a commercial species that commands high prices in the market. We feel that not enough is known about the management of this species. In particular, not enough is known about its growth pattern. Thus, we model the length–weight relationship of this resource for each harvest site. We use regression models with factor-by-curve interactions. Specifically, a global test to compare regression curves and their derivatives between levels and a local test to draw inferences about critical points are provided.

Estimator Deret Fourier Dalam Regresi Nonparametrik dengan Pembobot Untuk Perencanaan Penjualan Camilan Khas Madura

The purpose of regression analysis is determining the relationship between response variables to predictor variables. To estimate the regression curve there are three approaches, parametric regression, nonparametric regression, and semiparametric regression. In this study, the estimator form of nonparametric regression curve is analyzed by using the Fourier series approach with sine and cosine bases, sine bases, and cosine bases. Based on Weighted Least Square (WLS) optimization, the estimator result can be applied to model the sale planning of Madura typical snacks. Nonparametric regression estimators with the Fourier series approach are weighted with uniform and variance weight. The best model that be obtained in this study for uniform weight, based on cosine and sine basis with GCV value ​​of 1541.015, MSE value of 0.1375912 and determination coefficient value of 0.4728418%. The best model for variance weight is based on cosine and sine basis with a GCV value of 1541.011, MSE value of 0.1375912 and determination coefficient of 0.4728227%.

Relationship of multi-biomarker disease activity score and other risk factors with radiographic progression in an observational study of patients with rheumatoid arthritis.

Objectives. To evaluate the multi-biomarker disease activity (MBDA) score as a predictor of radiographic progression and compare it with other risk factors among patients with established RA receiving non-biologic DMARDs.Methods. For 163 patients with RA, we assessed 271 visits for MBDA score (scale of 1−100), clinical data and subsequent 1-year radiographic progression (change in Sharp−van der Heijde score [SHS]). Scatter plot and non-parametric quantile regression curves evaluated the relationship between the MBDA score and change in SHS. Changes in joint space narrowing and erosions were compared among MBDA categories with Wilcoxon rank-sum tests. The ability of the MBDA score to independently predict progression was determined by multivariate models and cross-classification of MBDA score with other risk factors. Generalized estimating equation methodology was used in model estimations to adjust for same-patient visits, always ≥1 year apart.Results. Patient characteristics included 67% female, 66%/67% RF+/anti-CCP+; mean age 55 years, MBDA score 43 (moderate = 30−44); median disease duration 4.6 years, SHS 23. Radiographic progression was infrequent for low MBDA scores. Relative risk for progression increased continuously as the MBDA score increased, reaching 17.4 for change in SHS >5 with MBDA scores ≥60. Joint space narrowing and erosion progression were associated with MBDA score. MBDA score was associated with radiographic progression after adjustments for other risk factors. MBDA score significantly differentiated risk for progression when swollen joint count, CRP or DAS28–CRP was low, and among seropositive patients.Conclusion. MBDA score enhanced the ability of conventional risk factors to predict radiographic progression in patients with established RA receiving non-biologic DMARDs.

Analysis of small intestinal transit and colon arrival times of non-disintegrating tablets administered in the fasted state

In this study individual data on tablet gastrointestinal transit times (i.e. gastric emptying, small intestinal transit, ileocecal junction residence, and colon arrival times) were obtained from literature in order to present and analyze their distributions and relationships. The influence of the time of food intake after tablet administration in fasted state on gastrointestinal transit times was additionally evaluated.There were 114 measurements from subjects who received the first meal at 4h after tablet administration. Approximately 32% of the tablets arrived into the colon before the meal intake at 4h. An evident increase in the frequency of colon arrival of tablets within 40min after the meal intake at 4h post-dose was observed, where approximately 39% of all tablets arrived into the colon. This is in accordance with findings described in literature where a meal ingested several hours post-dose accelerates tablet transit through the terminal ileum and shortens the transit through the small intestine. The median (min, max) of gastric emptying, small intestinal transit, and colon arrival times in the group where the first meal intake was at 4h post-dose is 35 (0,192), 215 (60,544), and 254 (117,604) minutes, respectively. The dependence of colon arrival times on gastric emptying times was described by the nonparametric regression curve, and compared with the presumed interval of colon arrival times, calculated by summation of observed gastric emptying times and frequently cited small intestinal transit time interval, i.e. 3–4h. For shorter gastric emptying times the trend of colon arrival times was within the presumed interval. At short gastric emptying times many observation points are also within the presumed interval since this interval coincides with short period after meal intake at 4h post-dose. Additionally, in numerous occasions relatively long ileocecal junction residence times were obtained, which may be important information from the point of view of drug absorption. The findings of gastrointestinal transit times are important and should be taken into consideration when predicting the in vivo performance of dosage forms after oral administration.

An Effective Nonparametric Quantile Regression Method for Solving the Crossing Problem in Data Fitting Process

Nonparametric quantile regression method can be used as the first choice for some biostatistical data. Since the nonparametric quantile regression curves are estimated individually, the quantile curves can cross, leading to an invalid distribution estimation for the response. A simple nonparametric quantile regression method is proposed to avoid the crossing problem. The method uses nonparametric conditional density function estimate instead of the conditional distribution estimate to assure quantile regression function monotonous. Both a simulation study and an analysis of real salmon lustrousness data show the significant improvement of the method in solving the quantile crossing problem for some kind of biological data.