Nonparametric Regression Model Research Articles

APPLIED MIXED KERNEL AND FOURIER SERIES MODELLING IN NONPARAMETRIC REGRESSION

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.

The Role of Body Mass Index on Physical Activity, Symptoms, and Related Outcomes Following Pediatric Concussion

To determine the step count and self-reported activity levels for obese and non-obese pediatric patients following concussion and predict self-reported symptoms, quality of life, and psychological health over time. Participants completed the Post-Concussion Symptom Scale (PCSS), Pediatric Quality of Life (PedsQL), and Behavioral Symptom Inventory-18 (BSI-18) at an initial visit (<72 hours), 3-5 days post-injury, 10-18 days post-injury, and 1 and 2 months post-injury. Physical activity data (eg, step count) were collected via a commercial actigraph. Participants were categorized into obese and non-obese body mass index (BMI) groups based on age- and sex-adjusted growth standards. Mann Whitney U tests compared groups while nonparametric series regression models examined the effect of obese BMI and average daily step count on PCSS, PedsQL, and BSI-18 outcomes at 1- and 2-months post-injury. 194 participants were included: 153 (78.9%; M=14.6 ± 2.4 years; 50% female) in the non-obese group and 41 (21.1%; M=14.2 ± 2.0 years; 44% female) in the obese group. The obese group had a 22.8% lower average daily step count in the week post-injury (p=0.02). At 2-months, there was a significant association between obese BMI and worse PCSS total score (p=0.042), PedsQL (p=0.017), and BSI-18 anxiety (p=0.046). Average daily step count in the first week post-injury was associated with a higher PCSS total score at 2 months (p=0.031). Pediatric patients following concussion with an obese BMI had a lower daily average step count in the week after injury and exhibited worse concussion symptoms, quality of life, and anxiety at 2 months compared with those with a non-obese BMI.

Spline Estimator in Nonparametric Ordinal Logistic Regression Model for Predicting Heart Attack Risk

In Indonesia, one of the main causes of death for both young and elderly people is heart attacks, and the main cause of heart attacks is non-communicable diseases such as hypertension. Deaths due to heart attacks caused by non-communicable diseases, namely hypertension, rank first in Indonesia. Therefore, predictions of the risk of having a heart attack caused by hypertension need serious attention. Further, for determining whether a patient is experiencing a heart attack, an effective method of prediction is required. One efficient approach is to use statistical models. This study discusses predicting risk of heart attack via modeling and classifying hypertension risk based on factors that influence it, namely, age, cholesterol levels, and triglyceride levels by using the spline estimator of the Nonparametric Ordinal Logistic Regression (NOLR) model. In this study, we assume an ordinal scale response variable with q categories to have an asymmetric distribution, namely, a multinomial distribution. The data used in this study are secondary data from medical records of cardiac poly patients at the Haji General Hospital in Surabaya, Indonesia. The results show that the proposed model approach has the greatest classification accuracy and sensitivity values compared to NOLR model approach using GAM, and the classical model approach, namely the Parametric Ordinal Logistic Regression (POLR) model. This means that the NOLR model approach is suitable for predicting hypertension and heart attack risks. Also, the NOLR model estimated using the LS-Spline estimator obtained is valid for predicting the risk of heart attack with accuracy value of 85% and sensitivity value of 100%.

The Estimating Parameter and Number of Knots for Nonparametric Regression Methods in Modelling Time Series Data

This research aims to explore and compare several nonparametric regression techniques, including smoothing splines, natural cubic splines, B-splines, and penalized spline methods. The focus is on estimating parameters and determining the optimal number of knots to forecast cyclic and nonlinear patterns, applying these methods to simulated and real-world datasets, such as Thailand’s coal import data. Cross-validation techniques are used to control and specify the number of knots, ensuring the curve fits the data points accurately. The study applies nonparametric regression to forecast time series data with cyclic patterns and nonlinear forms in the dependent variable, treating the independent variable as sequential data. Simulated data featuring cyclical patterns resembling economic cycles and nonlinear data with complex equations to capture variable interactions are used for experimentation. These simulations include variations in standard deviations and sample sizes. The evaluation criterion for the simulated data is the minimum average mean square error (MSE), which indicates the most efficient parameter estimation. For the real data, monthly coal import data from Thailand is used to estimate the parameters of the nonparametric regression model, with the MSE as the evaluation metric. The performance of these techniques is also assessed in forecasting future values, where the mean absolute percentage error (MAPE) is calculated. Among the methods, the natural cubic spline consistently yields the lowest average mean square error across all standard deviations and sample sizes in the simulated data. While the natural cubic spline excels in parameter estimation, B-splines show strong performance in forecasting future values.

Evaluation of the Performance of Kernel Non-parametric Regression and Ordinary Least Squares Regression

Researchers need to understand the differences between parametric and nonparametric regression models and how they work with available information about the relationship between response and explanatory variables and the distribution of random errors. This paper proposes a new nonparametric regression function for the kernel and employs it with the Nadaraya-Watson kernel estimator method and the Gaussian kernel function. The proposed kernel function (AMS) is then compared to the Gaussian kernel and the traditional parametric method, the ordinary least squares method (OLS). The objective of this study is to examine the effectiveness of nonparametric regression and identify the best-performing model when employing the Nadaraya-Watson kernel estimator method with the proposed kernel function (AMS), the Gaussian kernel, and the ordinary least squares (OLS) method. Additionally, it determines which method yields the most accurate results when analyzing nonparametric regression models and provides valuable insights for practitioners looking to apply these techniques in real-world scenarios. However, criteria such as generalized cross-validation (GCV), mean square error (MSE), and coefficient determination are used to select the most efficient estimated model. Simulated data was used to evaluate the performance and efficiency of estimators using different sample sizes. The results favorable the simulation illustrate that the Nadaraya-Watson kernel estimator using the proposed kernel function (AMS) exhibited favorable and superior performance compared to other methods. The coefficients of determination indicate that the highest values attained were 98%, 99%, and 99%. The proposed function (AMS) yielded the lowest MSE and GCV values across all samples. Therefore, this suggests that the model can generate precise predictions and enhance the performance of the focused data.

Improved confidence intervals for nonlinear mixed-effects and nonparametric regression models

Improved confidence intervals for nonlinear mixed-effects and nonparametric regression models

The convergence properties for randomly weighted sums of widely negative dependent random variables under sub-linear expectations with related statistical applications

In this paper, we study the complete convergence and complete moment convergence for randomly weighted sums of arrays of rowwise widely negative dependent random variables in sub-linear expectation space under some appropriate conditions, which extend and improve the corresponding ones in classical probability space to the case of sub-linear expectation space. And we obtain a strong law of large numbers for the randomly weighted sums of arrays of rowwise widely negative dependent random variables. As applications of our main results, we not only present a result on the complete consistency for the weighted estimator in a nonparametric regression model, but also obtain the complete consistency for the least squares estimators in errors-in-variables regression models based on widely negative dependent errors under sub-linear expectations. We perform some numerical simulations to verify the validity of the theoretical results and a real example is analysed for illustration.

Detecting Age Prone to Growth Retardation in Children Through a Bi-Response Nonparametric Regression Model with a Penalized Spline Estimator.

The growth of children aged 0-60 months can impact their subsequent growth and development. This study aims to identify the vulnerable age for boys and girls, who experience growth retardation within this age range. The study design used was a cross-sectional approach in which each child's measurement data was only taken once. The data were obtained from weighing results at the Health Integrated Service Post in South Sulawesi Province in 2022. The number of data analyzed was 698 children, namely 369 boys and 329 girls by considering the factors of age, weight, and height. We used a nonparametric bi-response regression model estimated using a penalized spline. The knots used are 12, 24, 36, and 48 on each model. The value of the penalized spline regression coefficient in the model indicates that the child's growth is slowed down and is not within normal limits. This can be seen in the weight and height of boys from the age of reaching 12 months to 24 months, only increasing by about 0.3 kg and 0.3 cm. For girls, the problem occurs from the age of 24 to 36 months, namely their weight increases by about 0.6 kg, and their height increases by about 1 cm. The analysis results show that boys' growth slows down at 2 years of age and continues until 5 years of age. In the case of girls, their growth begins to slow when they are 3 years old until they reach 5 years old.

Strong laws for weighted sums of widely orthant dependent random variables and applications

Abstract In this study, the strong law of large numbers and the convergence rate for weighted sums of non-identically distributed widely orthant dependent random variables are established. As applications, the strong consistency for weighted estimator in nonparametric regression model and the rate of strong consistency for least-squares estimator in multiple linear regression model are obtained. Some numerical simulations are also provided to verify the validity of the theoretical results.

Statistical inference on nonparametric regression model with approximation of Fourier series function: Estimation and hypothesis testing

Nonparametric regression is an approximation method in regression analysis that is not constrained by the assumption of knowing the regression curve. One of the functions to approximate the curve is a Fourier series function. The nonparametric regression model with approximation of a Fourier series function has been widely discussed by several researchers. However, discussions on statistical inference, particularly in partial hypothesis testing, has not been carried out previously. Therefore, the purpose of this research is to discuss the statistical inference on nonparametric regression model with approximation of a Fourier series function. The discussion includes parameter and model estimations, simultaneous and partial hypotheses testing. In the application, we use life expectancy data from East Java Province during 2022. Based on data analysis, we obtain a model estimation with an R-square value of 96.24 %. At a 5 % significance level, the parameters simultaneously have a significant influence on the model. Partially, four parameters are not significant. However, overall, the predictor variables significantly influence the life expectancy data.•The Fourier series function used is a Fourier series function introduced by Bilodeau (1992).•The model estimation is obtained by selecting the optimal number of oscillation parameters.•The statistical test is obtained using the LRT method.

On complete convergence for weighted sums of m-widely acceptable random variables under sub-linear expectations and its statistical applications

. In this article, by means of Rosenthal-type inequality, we study the complete convergence and strong law of large numbers for weighted sums of m-widely accpetable random variables under sub-linear expectations, which extend some existing results in classical probability space. As applications, we investigate the complete consistency and strong consistency of weighted estimators in nonparametric regression models under sub-linear expectations. In addition, we provide some simulation studies to verify the finite sample performance of the theoretical results.

Robust tests for equality of regression curves based on characteristic functions

This paper focuses on the problem of testing the null hypothesis that the regression functions of several populations are equal under a general nonparametric homoscedastic regression model. It is well known that linear kernel regression estimators are sensitive to atypical responses. These distorted estimates will influence the test statistic constructed from them so the conclusions obtained when testing equality of several regression functions may also be affected. In recent years, the use of testing procedures based on empirical characteristic functions has shown good practical properties. For that reason, to provide more reliable inferences, we construct a test statistic that combines characteristic functions and residuals obtained from a robust smoother under the null hypothesis. The asymptotic distribution of the test statistic is studied under the null hypothesis and under root − n contiguous alternatives. A Monte Carlo study is performed to compare the finite sample behaviour of the proposed test with the classical one obtained using local averages. The reported numerical experiments show the advantage of the proposed methodology over the one based on Nadaraya–Watson estimators for finite samples. An illustration to a real data set is also provided and enables to investigate the sensitivity of the p − value to the bandwidth selection.

MODELING DHF IN CENTRAL JAVA USING HYBRID NONPARAMETRIC SPLINE TRUNCATED-FOURIER SERIES APPROACH

Regression analysis aims to determine the relationship and influence of predictor variables on response variables through regression curve. The problem with nonparametric regression research so far is that it only uses one approach, causing the estimation results to be biased, even though each data sub-pattern has its own suitability depending on the approach method used. Therefore, the hybrid method emerged as a development of nonparametric regression. Hybrid models are models that combine approach methods, with the hope of increasing accuracy in modeling analysis. This research was carried out using two non-parametric approaches, namely Spline Truncated and Fourier Series. Dengue Hemorrhagic Fever (DHF) is a disease caused by the dengue virus. DHF is endemic and occurs throughout the year, especially during the rainy season because mosquitoes reproduce optimally. The aim of this research is to estimate the Hybrid Nonparametric Spline Truncated -Fourier Series model and apply the estimation results to data on DHF cases in Central Java. The data used to apply the hybrid nonparametric Spline Truncated-Fourier series regression model is DHF in the city/districts of Central Java. Estimation smoothing parameters uses the GCV (Generalized Cross Validation) method. The best model is selected based on largest R-Square and the smallest MSE. Modeling the disease of DHF cases in Central Java using the Spline Truncated-Fourier Series hybrid estimator produced the best model from the Spline Truncated model with two knot points for each predictor and the Fourier Series model with value of 9. Based on the results obtained, it can be compared that the Truncated Spline-Fourier Series hybrid model is better than the Spline Truncated model, this can be seen from the largest R-square, namely 99.94% and the smallest MSE.

Spiritual needs and influencing factors among people with stroke in China: a cross-sectional study

BackgroundStroke is one of the primary causes of disability in China and around the world, having an impact on the health and well-being of stroke patients. The importance of spiritual needs for stroke patients has always been a controversial topic internationally, partly because related research was mostly qualitative and may not directly reflect the degree of spiritual needs. In addition, most studies focus on the same cultural background, there is a lack of research that delves into the nuances of Chinese culture and background. The goal of this study is to evaluate the level of spiritual needs and influencing factors in Chinese stroke patients and to explore the mediating role and pathways of these variables on spiritual needs.MethodsFrom August 2022 to January 2023, we conducted a cross-sectional questionnaire survey of 422 stroke patients in the affiliated hospitals of Hunan University of Chinese Medicine in Changsha Province by cluster sampling. We measured the patient’s spiritual needs, quality of life, anxiety and depression levels, and family support using the Spiritual Needs Questionnaire (SPNQ), the MOS36 item Short Form Health Survey (SF-36), the Hospital Anxiety and Depression Scale (HADS), and the Family Support Self Rating Scale (PSS-Fa). We used the General Information Questionnaire to gain insight into the sociodemographic characteristics of the patients. Nonparametric tests and multiple linear regression models were used to analyze the independent relationship between spiritual needs and quality of life, anxiety, depression, and family support. The mediation model in AMOS 24.0 software was used to analyze the mediating role among the five variables.ResultsThe score of spiritual needs of people with stroke included in this study was 37 points [IQR 33 to 40)]. The influencing factors of spiritual needs included primary economic sources for disease-related expenditures (p = 0.044), number of stroke occurrences (p = 0.001), duration of illness (p = 0.023), activities of daily living (p = 0.006), depression scores(p = 0.034), and family support scores(p = 0.008). Anxiety (β = 0.347, p = 0.004), depression (β = 0.368, p = 0.005), and family support (β = 0.167, p = 0.023) had directly or indirectly affected the spiritual needs of people with stroke. Quality of life (β=-0.202, p = 0.017) had a direct effect on spiritual needs.ConclusionsThe spiritual needs of people with stroke were at an intermediate level. Our findings highlight that the SPNQ score is associated with anxiety, depression, quality of life, and family support. Therefore, nurses should identify the spiritual needs of patients and provide them with effective and comprehensive spiritual care by reducing negative emotions and enhancing social support, promoting the development and progress of spiritual care in China. This study offers a theoretical basis for the spiritual care of clinical people with stroke and constructing a stroke spiritual care model.

The Berry-Esseen bounds of wavelet estimator for nonparametric regression models whose errors form a linear process based on ANA sequences

In this paper, we consider the nonparametric regression model Y ni = g ( t ni ) + ϵ i ( 1 ≤ i ≤ n ), where ϵ i = ∑ j = − ∞ ∞ a j e i − j and e i are identically distributed and asymptotically negatively associated (ANA or ρ − , for short) sequences. This paper obtains the Berry-Esseen bounds of the wavelet estimator of g ( ⋅ ) , and the rate of the normal approximation is shown as O ( n − 1 / 4 ) under certain conditions. Finally, the simulation study is provided to verify the validity of the theoretical results.

Nonparametric Regression Modeling with Multivariable Fourier Series Estimator on Average Length of Schooling in Central Java in 2023

Nonparametric Regression Modeling with Multivariable Fourier Series Estimator on Average Length of Schooling in Central Java in 2023

Selection of optimal knot point and best geographic weighted on geographically weighted spline nonparametric regression model

This study proposes the development of a nonparametric regression model combined with geographically weighted regression. The regression model considers geographical factors and has a data pattern that does not follow a parametric form to overcome the problem of spatial heterogeneity and unknown regression functions. This study aims to model provincial food security index data in Indonesia with the GWSNR model, so finding the optimal knot point and the best geographic weighting is necessary. We propose the selection of optimal knot points using the Cross Validation (CV) and Generalized Cross Validation (GCV) methods. The optimal knot point will control the accuracy of the regression curve as we also consider the MSE value in showing the ability of the model. In addition, we determine the best geographic weighting and test the significance of the model parameters. We demonstrate the GWSNR model on food security index data. The best GWSNR model uses the Gaussian kernel weighting function and selects the optimal knot point as one-knot point based on the lowest CV and GCV values. Simultaneous and partial parameter test results show that there are 10 area classifications with different effects on each group of classification results. Some of the highlights of the proposed approach are:•The method is the development of a nonparametric regression model with geographic weighting, which combines nonparametric and spatial regression in modeling the national food security index.•There are three-knot points tested in nonparametric truncated spline regression and three geographic weightings in spatial regression. Then the optimal knot point and best bandwidth are determined using Cross Validation and Generalized Cross Validation.•This article will determine regional groupings in Indonesia in 2022 based on significant predictors in modeling the national food security index numbers.

Can the Upper Vermilion and the Nasolabial Fold Be Changed With Orthognathic Surgery?

BackgroundRetrusive profiles show an appearance of aging with an under-projected vermilion and pronounced nasolabial folds due to deficient bone support. PurposeA study was made of the association between orthognathic surgery and changes in the nasolabial and vermilion areas in patients with retrusive profiles. Study design, setting, sampleA retrospective cohort study evaluated patients subjected to bimaxillary surgery according to the Barcelona Line (BL) protocol during 2021 at Teknon Medical Center (Barcelona, Spain). Subjects with craniofacial syndromes, facial aesthetic procedures, and dental rehabilitations involving lip changes, were excluded. Predictor variableThe predictor variable was the timing of cephalometric measures, reported as T0 (preoperatively), T1 (one month after surgery), and T2 (after one year of follow-up). Main outcome variableThe outcome variable corresponded to the soft tissue changes of the nasolabial and vermilion area, reported as the nasolabial fold length and angle, nasolabial angle, upper lip concavity, vermilion length, and upper lip sagittal distance from BL. CovariatesThe covariates comprised patient demographic data, the surgical-orthodontic protocol, and the magnitude and direction of the skeletal movements. AnalysesDescriptive and inferential analyses were performed based on analysis of variance (ANOVA), the Bonferroni test, Pearson’s linear coefficient, the nonparametric Mann-Whitney U-test, Kruskal-Wallis test, and multiple linear regression models. Statistical significance was considered for p < 0.05. ResultsThe sample comprised 27 subjects with a mean age of 32.5 ± 11.2 years. A mean decrease in nasolabial angle of 5.5 ± 6º was recorded (p < 0.001), with a shortening of the nasolabial fold length of 4.4 ± 7.6 mm (p=0.019). An increase in upper lip concavity angle of 14.4 ± 12º was recorded (p < 0.001), along with a vermilion lengthening of 1.6 ± 1.3 mm (p < 0.001) and an increase in upper lip sagittal distance to BL of 5.7 ± 7.3 mm (p=0.001), indicating a more projected and everted upper vermilion. Conclusions and relevanceWhen adequate dentoskeletal support is provided by specific positional changes of the jaws planned through orthognathic surgery, the length of the nasolabial fold decreases, and the upper vermilion lengthens and becomes slightly everted.

Stunting Prevalence Modeling Using Nonparametric Regression of Quadratic Splines

The nonparametric regression approach is used when the shape of the regression curve between the response variable and the predictor variable is assumed to be of unknown shape. The advantages of nonparametric regression have high flexibility. A nonparametric regression approach that is often used is truncated spline which has an excellent ability to handle data whose behavior changes at certain sub-sub intervals. The purpose of this study is to obtain the best model of multivariable nonparametric regression with linear and quadratic truncated spline approaches using the Generalized Cross Validation (GCV) and Unbiased Risk (UBR) methods and to find out the factors that influence the prevalence of stunting in Indonesia in 2021. The data used were the prevalence of stunting as a response variable and the predictor variable used was the percentage of infants receiving exclusive breastfeeding for 6 months, the percentage of households that have proper sanitation, the percentage of toddlers who get Early Initiation of Breastfeeding (IMD), the percentage of poor people, and the percentage of pregnant women at risk of SEZ. The results showed that the best quadratic truncated spline nonparametric regression model in modeling stunting prevalence was quadraic truncated spline using the GCV method with three knot points. This model has a minimum GCV value of 7.29 with an MSE value of 1.82 and a R2 value of 94.07%.

Nonparametric screening for additive quantile regression in ultra-high dimension

In practical applications, one often does not know the ‘true’ structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal nonparametric screening methods have been recently developed. However, these approaches may miss important covariates that are marginally independent of the response, or may select unimportant covariates due to their high correlations with important covariates. To mitigate such shortcomings, we develop a conditional nonparametric quantile screening procedure (complemented by subsequent selection) for nonparametric additive quantile regression models. Under some mild conditions, we show that the proposed screening method can identify all relevant covariates in a small number of steps with probability approaching one. The subsequent narrowed best subset (via a modified Bayesian information criterion) also contains all the relevant covariates with overwhelming probability. The advantages of our proposed procedure are demonstrated through simulation studies and a real data example.