Nonparametric Regression Model Research Articles

Optimal smoothing parameter selection in single-index model derivative estimation

. Single-index model is one of the most popular semiparametric models in applied econometrics. Estimation of the derivative function is often of crucial importance, as studying “marginal effects” serves as a cornerstone of microeconomics. A prerequisite for the successful application of nonparametric/semiparametric kernel estimation methods is to select smoothing parameters properly to balance the estimation squared bias and variance. Henderson et al. (2015) propose a novel method for selecting the smoothing parameters optimally for derivative function estimation. However, their method suffers from the “curse of diemnsionality” problem in a multivariate nonparametric regression model. In this article, we extend the work of Henderson et al. (2015) to estimation of the derivative function of a single-index model. Specifically, we propose a data-driven method to select smoothing parameters optimally for single-index model derivative function estimation. We also derive the asymptotic distribution of the resulting local linear estimator of the derivative function. Both simulations and empirical applications show that the proposed method works well in practice.

Partially fixed bayesian additive regression trees

Bayesian Additive Regression Trees (BART) is a widely popular nonparametric regression model known for its accurate prediction capabilities. In certain situations, there is knowledge suggesting the existence of certain dominant variables. However, the BART model fails to fully utilize the knowledge. To tackle this problem, the paper introduces a modification to BART known as the Partially Fixed BART model. By fixing a portion of the trees' structure, this model enables more efficient utilization of prior knowledge, resulting in enhanced estimation accuracy. Moreover, the Partially Fixed BART model can offer more precise estimates and valuable insights for future analysis even when such prior knowledge is absent. Empirical results substantiate the enhancement of the proposed model in comparison to the original BART.

Marijuana Use Increases Risk of Hematoma Formation in Patients Undergoing Abdominal Body Contouring Surgery

Abstract Goals/Purpose The physiological effect of marijuana is thought to include platelet inhibition and poor wound healing, however, there is mixed clinical evidence in the plastic surgery literature regarding this topic. As marijuana usage continues to increase, this study sought to identify the effect of marijuana on postoperative complication rates in patients undergoing abdominal body contouring surgery (ABCS) while controlling for tobacco consumption and other comorbidities. Methods/Technique A retrospective cohort study was conducted in patients who underwent panniculectomy or abdominoplasty at our institution between 2016 and 2021. Patients were separated into groups of active (at time of surgery), former, and no marijuana use. Demographic characteristics, smoking history, laboratory results, comorbidities, operative details, and postoperative complications including hematoma, deep vein thrombosis (DVT) and pulmonary embolism (PE), and wound healing complications were analyzed. Parametric, nonparametric, and multivariable regression modeling was used for analysis. Results/Complications 815 patients who underwent panniculectomy or abdominoplasty were included in the study. 61 patients (7.5%) reported active marijuana use at time of their surgery, and 31 patients (3.8%) reported former marijuana use (defined as last use >2 months prior). Patients who reported any marijuana use were significantly younger (40.5 years vs 45.9 years; p<0.0001) and more likely to identify as Black (OR=2.34; p=0.005). Any marijuana use was significantly associated with reported tobacco use (OR=4.80; p<0.001; 95% CI 1.69-12.69) After adjusting for age, BMI, tobacco use, platelet count, and comorbidity index, active marijuana use was associated with significantly higher risk of hematoma formation (OR=2.55; P= 0.03; 95% CI 1.12-6.55) as well as any complication combined (OR=1.73; p=0.02, 95% CI 1.15-3.56). Other complications, including venous thromboembolism, infection, seroma, umbilical necrosis, wound dehiscence, or anesthetic-related complications were not significantly associated with reported marijuana use. Conclusion When controlling for multiple confounders, marijuana use appears to be independently associated with increased risk of hematoma development in patients undergoing abdominal body contouring surgery with either abdominoplasty or panniculectomy. Further research is warranted to investigate the exact relationships and mechanisms of action behind this finding.

Roles of Hospital Type and Community Setting in Rate of Screening for Metabolic Disorders Among Psychiatric Patients.

Globally, rates of metabolic disorders continue to climb, leading to significant disease morbidity and mortality. Individuals with mental illness are particularly prone to obesity, and some medications, such as antipsychotics, may increase the risk for metabolic disorders. The American Psychiatric Association and the American Diabetes Association recommend that patients taking antipsychotic medications receive regular screening for metabolic disorders. This study examined hospital and community factors associated with screening these patients for such disorders. The authors combined Centers for Medicare and Medicaid Services (CMS) hospital-level data on screening for metabolic disorders among patients with an antipsychotic prescription with community data, including urbanization classification, social vulnerability, and metabolic disease presence and risk factors. Data were merged at the county level and evaluated with a nonparametric multivariate regression model. The CMS data set included 1,497 U.S. hospitals with data on screening for metabolic disorders among patients with an antipsychotic prescription. Screening rates varied by type of facility; acute care and critical access hospitals outperformed freestanding psychiatric facilities (p<0.001). No other variables examined in the multivariate model were associated with screening for metabolic disorders. Despite common resource limitations, screening for metabolic disorders may be driven more by logistics and less by time, finances, or a community's primary care network. Identifying the specific logistical challenges of freestanding psychiatric facilities could aid in the development of targeted interventions to improve the rates of screening for and treatment of not only metabolic disorders but also other common comorbid conditions.

Effects of esketamine nasal spray on depressive symptom severity in adults with treatment-resistant depression and associations between the Montgomery-Åsberg Depression Rating Scale and the 9-item Patient Health Questionnaire.

To examine the effect of esketamine nasal spray (ESK) plus newly initiated oral antidepressant (OAD) versus OAD plus placebo nasal spray (PBO) on the association between Montgomery-Åsberg Depression Rating Scale (MADRS) and 9-item Patient Health Questionnaire (PHQ-9) scores in adults with treatment-resistant depression (TRD). Data from TRANSFORM-1 and TRANSFORM-2 (two similarly designed, randomized, active-controlled TRD studies) and SUSTAIN-1 (relapse prevention study) were analyzed. Group differences for mean changes in PHQ-9 total score from baseline were compared using analysis of covariance. Associations between MADRS and PHQ-9 total scores from TRANSFORM-1/TRANSFORM-2 were assessed using simple parametric, nonparametric, and multiple regression models. In TRANSFORM-1/TRANSFORM-2 (ESK+OAD, n=343; OAD+PBO, n=222), baseline PHQ-9 mean scores were 20.4 for ESK+OAD and 20.6 for OAD+PBO (severe depression). At day 28, significant group differences were observed in least squares mean change (SE) in PHQ-9 scores from baseline (-12.8 [0.46] vs -10.3 [0.53], P<.001) and in clinically substantial change in PHQ-9 scores (≥6 points; 77.1% vs 64%, P<.001) in ESK+OAD and OAD+PBO groups, respectively. A nonlinear relationship between MADRS and PHQ-9 was observed; total scores demonstrated increased correlation over time. In SUSTAIN-1, 57.3% of patients receiving ESK+OAD (n=89) versus 44.2% receiving OAD+PBO (n=86) retained remission status (PHQ-9 score ≤4) at maintenance treatment end point (P=.044). In adults with TRD, ESK+OAD significantly improved severity of depressive symptoms, and more patients achieved clinically meaningful changes in depressive symptoms based on PHQ-9, versus OAD+PBO. PHQ-9 outcomes were consistent with those of clinician-rated MADRS. ClinicalTrials.gov: NCT02417064, NCT02418585, NCT02493868.

Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator

In data analysis using a nonparametric regression approach, we are often faced with the problem of analyzing a set of data that has mixed patterns, namely, some of the data have a certain pattern and the rest of the data have a different pattern. To handle this kind of datum, we propose the use of a mixed estimator. In this study, we theoretically discuss a developed estimation method for a nonparametric regression model with two or more response variables and predictor variables, and there is a correlation between the response variables using a mixed estimator. The model is called the multiresponse multipredictor nonparametric regression (MMNR) model. The mixed estimator used for estimating the MMNR model is a mixed estimator of smoothing spline and Fourier series that is suitable for analyzing data with patterns that partly change at certain subintervals, and some others that follow a recurring pattern in a certain trend. Since in the MMNR model there is a correlation between responses, a symmetric weight matrix is involved in the estimation process of the MMNR model. To estimate the MMNR model, we apply the reproducing kernel Hilbert space (RKHS) method to penalized weighted least square (PWLS) optimization for estimating the regression function of the MMNR model, which consists of a smoothing spline component and a Fourier series component. A simulation study to show the performance of proposed method is also given. The obtained results are estimations of the smoothing spline component, Fourier series component, MMNR model, weight matrix, and consistency of estimated regression function. In conclusion, the estimation of the MMNR model using the mixed estimator is a combination of smoothing spline component and Fourier series component estimators. It depends on smoothing and oscillation parameters, and it has linear in observation and consistent properties.

Fair Multivariate Adaptive Regression Splines for Ensuring Equity and Transparency

Predictive analytics has been widely used in various domains, including education, to inform decision-making and improve outcomes. However, many predictive models are proprietary and inaccessible for evaluation or modification by researchers and practitioners, limiting their accountability and ethical design. Moreover, predictive models are often opaque and incomprehensible to the officials who use them, reducing their trust and utility. Furthermore, predictive models may introduce or exacerbate bias and inequity, as they have done in many sectors of society. Therefore, there is a need for transparent, interpretable, and fair predictive models that can be easily adopted and adapted by different stakeholders. In this paper, we propose a fair predictive model based on multivariate adaptive regression splines (MARS) that incorporates fairness measures in the learning process. MARS is a non-parametric regression model that performs feature selection, handles non-linear relationships, generates interpretable decision rules, and derives optimal splitting criteria on the variables. Specifically, we integrate fairness into the knot optimization algorithm and provide theoretical and empirical evidence of how it results in a fair knot placement. We apply our fairMARS model to real-world data and demonstrate its effectiveness in terms of accuracy and equity. Our paper contributes to the advancement of responsible and ethical predictive analytics for social good.

Hypothesis Testing for Class-Conditional Noise Using Local Maximum Likelihood

In supervised learning, automatically assessing the quality of the labels before any learning takes place remains an open research question. In certain particular cases, hypothesis testing procedures have been proposed to assess whether a given instance-label dataset is contaminated with class-conditional label noise, as opposed to uniform label noise. The existing theory builds on the asymptotic properties of the Maximum Likelihood Estimate for parametric logistic regression. However, the parametric assumptions on top of which these approaches are constructed are often too strong and unrealistic in practice. To alleviate this problem, in this paper we propose an alternative path by showing how similar procedures can be followed when the underlying model is a product of Local Maximum Likelihood Estimation that leads to more flexible nonparametric logistic regression models, which in turn are less susceptible to model misspecification. This different view allows for wider applicability of the tests by offering users access to a richer model class. Similarly to existing works, we assume we have access to anchor points which are provided by the users. We introduce the necessary ingredients for the adaptation of the hypothesis tests to the case of nonparametric logistic regression and empirically compare against the parametric approach presenting both synthetic and real-world case studies and discussing the advantages and limitations of the proposed approach.

The performance of mixed truncated spline-local linear nonparametric regression model for longitudinal data

A mixed estimator nonparametric regression (MENR) model is an additive model that involves a combination of two estimators or more in multivariable nonparametric regression. The model is used when there are differences in data patterns among predictor variables. This study proposes the development of the MENR model on longitudinal data namely a mixed truncated spline-local linear nonparametric regression (MTSLLNR) model. A modified weighted least square (WLS) method through two-stage estimation is used to estimate the regression function in the proposed model. To illustrate the performance of the MTSLLNR model, a simulation study with a sample size variation of subjects and time points is provided. Additionally, the MTSLLNR model is also applied to model the poverty gap index data. Both simulated and real data results suggest that the proposed model has consistency findings and good performance in longitudinal data modeling. Some highlights of the proposed method are:•The method combines two estimators of local linear and truncated spline to accommodate the differences in data patterns in the nonparametric regression for longitudinal data.•Selection of optimal knots and bandwidth using the generalized cross-validation (GCV) method.•The consistency findings and general performance of the method is shown by simulation and real data application.

A Comparison Between Local Linear Regression and K- Nearest Neighbor Methods in Estimating the Nonparametric Regression Model with Simulation and Application

In this paper, the nonparametric regression model was estimated using two common estimation methods (Local Linear Regression Estimator (LLRE) and K-Nearest Neighbor Estimator (KNNE). The simulation process was conducted using the statistical programming language, R, for these methods, and they were compared using the Average Root Mean Squares Error (ARMSE) criterion, with three sample sizes (50, 100, 150), three levels of error variance (0.3, 0.7, 1) and two non-linear models. The results for the first model showed the superiority of the nearest neighbor estimator (KNNE) method in most cases, and for the second model the local linear regression estimator (LLRE) was superior at all sample sizes and for all levels of variance. On the applied side, the effect of hemoglobin (Hb) on the packed cell volume (PCV) of 150 patients with chronic kidney disease was studied. The estimation process was made using the two methods, and the comparison between them was made using the root mean square error (RMSE) criterion. It was shown through the results of the applied side that the preference was for the nearest neighbor estimator (KNNE) method.

Parametric and Nonparametric Approaches of Reid Vapor Pressure Prediction for Gasoline Containing Oxygenates: A Comparative Analysis Using Partial Least Squares, Nonlinear, and LOWESS Regression Modelling Strategies with Physical Properties

This study provides insights into the challenges involved in predicting the Reid vapor pressure (RVP) of gasoline-oxygenate blends (GOB), which is an important indicator of fuel quality and compliance with environmental and performance standards. Given the enormous variety of gasoline compositions and ratios available, there is a significant demand for a fast, straightforward, and cost-effective technique to predict RVP without relying on costly instruments or complicated spectral measurements that involve numerous input variables. A comparative performance analysis has been performed for different regression modelling strategies for predicting RVP in GOB, which is valuable for researchers and practitioners in the petroleum industry for saving time and money. Parametric and nonparametric approaches were compared using partial least squares regression (PLSR), nonlinear regression (NLR), and nonparametric regression (NPR) models. Locally weighted scatterplot smoothing (LOWESS) approach was applied to the NPR model. The gasoline’s physical characteristics (distillation curves and density) formed the basis for the analysis of these models’ performances. Acceptable error metrics have been reached for root mean square error of calibration and prediction (RMSEC and RMSEP) values, for the PLSR, NLR, and NPR models, which are 4.790, 6.235, 4.739, 6.149, 3.968, and 6.029, respectively, which are close for those reported in literature. The NPR model eliminates parametric constraints and allows for a different kind of data structure to emerge. The established models here demonstrate a sound ability to overcome barriers by omitting the use of inconvenient spectral measurements to save expense and simplify data calibration, making them a promising approach for RVP detection of GOB. This finding aids in the development of more accurate RVP prediction models and contributes to the optimization of fuel formulations.

Investigating Growth-at-Risk Using a Multicountry Nonparametric Quantile Factor Model

We develop a nonparametric quantile panel regression model. Within each quantile, the quantile function is a combination of linear and nonlinear parts, which we approximate using Bayesian Additive Regression Trees (BART). Cross-sectional information is captured through a conditionally heteroscedastic latent factor. The nonparametric feature enhances flexibility, while the panel feature increases the number of observations in the tails. We develop Bayesian methods for inference and apply several versions of the model to study growth-at-risk dynamics in a panel of 11 advanced economies. Our framework usually improves upon single-country quantile models in recursive growth forecast comparisons.

MODELING OPEN UNEMPLOYMENT RATE IN KALIMANTAN ISLAND USING NONPARAMETRIC REGRESSION WITH FOURIER SERIES ESTIMATOR

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.

A novel model of divergent predictive perception.

Predictive processing theories state that our subjective experience of reality is shaped by a balance of expectations based on previous knowledge about the world (i.e. priors) and confidence in sensory input from the environment. Divergent experiences (e.g. hallucinations and synaesthesia) are likely to occur when there is an imbalance between one's reliance on priors and sensory input. In a novel theoretical model, inspired by both predictive processing and psychological principles, we propose that predictable divergent experiences are associated with natural or environmentally induced prior/sensory imbalances: inappropriately strong or inflexible (i.e. maladaptive) high-level priors (beliefs) combined with low sensory confidence can result in reality discrimination issues, a characteristic of psychosis; maladaptive low-level priors (sensory expectations) combined with high sensory confidence can result in atypical sensory sensitivities and persistent divergent percepts, a characteristic of synaesthesia. Crucially, we propose that whether different divergent experiences manifest with dominantly sensory (e.g. hallucinations) or nonsensory characteristics (e.g. delusions) depends on mental imagery ability, which is a spectrum from aphantasia (absent or weak imagery) to hyperphantasia (extremely vivid imagery). We theorize that imagery is critically involved in shaping the sensory richness of divergent perceptual experience. In sum, to predict a range of divergent perceptual experiences in both clinical and general populations, three factors must be accounted for: a maladaptive use of priors, individual level of confidence in sensory input, and mental imagery ability. These ideas can be expressed formally using nonparametric regression modeling. We provide evidence for our theory from previous work and deliver predictions for future research.

Nonparametric estimation and forecasting of interval-valued time series regression models with constraints

Nowadays information technology advances allow the collecting and storage of large complex datasets in many areas. Modeling and forecasting interval-valued time series (ITS) has drawn much attention over the last two decades because interval-valued observations contain more information than point-valued observations over the same period and remove undesirable noises in high-frequency data. However, most work mainly focuses on modeling a linear univariate ITS or bivariate point process. This paper proposes nonparametric regression models for interval-valued time series with imposing constraints, e.g., monotonicity. This setting with a monotonic constraint is consistent with the existing literature, which focuses on incorporating valuable empirical information in modeling and forecasts. Two constraint estimators are developed and asymptotic properties are established. Monte Carlo simulation is conducted to show the finite sample performance. An empirical application to equity premium documents that the proposed model yields a better forecast performance than some popular models in the literature.

Some strong convergence properties for randomly weighted maximum partial sums of END random variables with statistical applications

This article mainly studies the strong convergence properties for randomly weighted maximum partial sums of arrays of row-wise extended negatively dependent (END, for short) random variables, including the complete moment convergence and complete f-moment convergence. The results obtained in this paper extend the corresponding ones in the literature. As an application, we investigate the complete consistency of the estimators of nonparametric regression models based on END random errors by using the complete convergence that we established. Then we provide comprehensive simulation studies to demonstrate the validity of the theoretical results based on the finite sample performance. Finally, an application to a real data set is illustrated.

A retrospective study of diameter and Breslow thickness in invasive melanomas.

A diameter larger than 6 millimeters is included in the criteria used in public health messages to detect a cutaneous melanoma. We aim to investigate the independent association of Breslow thickness with the melanoma diameter. A retrospective study was performed in patients with invasive melanomas of the nodular melanoma or superficial spreading melanoma subtype. The quartiles of the diameter (lower, median, upper) were studied in non-parametric quantile regression model. In total, 537 cases of invasive melanomas were included and 60% had Breslow thickness ≤ 1.0 mm. There were 429 SSM (79.9%) and 108 NM (20.1%). Although NMs were significantly thicker (median Breslow thickness: 2.7 mm versus 0.7 mm respectively, p<0.0001), they were not associated with larger diameter compared to SSMs (p:0.71). After adjustment for age and sex, melanoma location and subtype, having Breslow thickness ≤ 1.0 mm was not significantly associated with the lower quartile, median and upper quartile of the diameter (p-values: 0.063, 0.083, and 0.791, respectively). In our study including melanomas of the NM or SSM subtype, Breslow thickness was not associated with the diameter, adding evidence to support the limitations of using diameter larger than 6 mm for the detection of invasive melanomas and indicating the potential of smaller melanomas to be thicker tumors.

PEMODELAN REGRESI NONPARAMETRIK SPLINE TRUNCATED KASUS KEJADIAN DIARE DI PROVINSI BALI

Nonparametric regression is a flexible approach used to determine the relationship between the predictor variable and the response variable is unknown. One method that can be used to estimate nonparametric regression models is the truncated spline. The truncated spline is an effective method to estimate nonparametric regression models due to its ability to adapt to the data's characteristics through knots. Truncated spline estimates its parameters with the maximum likelihood estimator (MLE) method and finds the optimal knot points with the minimum generalized cross validation (GCV) value. This study used the truncated spline to model diarrhea cases in Bali Province, examining five variables that could affect incidence. The optimal knot points were 2-1-3-3-2 with a minimum GCV value of  67572,38. The study found that the number of clean drinking water facilities, food management places that meet health requirements, public places that meet health requirements, population density, and access to proper sanitation facilities had a significant effect on diarrhea incidence. The coefficient of determination for this model is 98,87%.

PEMODELAN REGRESI NONPARAMETRIK DENGAN ESTIMATOR SPLINE POLYNOMIAL TRUNCATED PADA DATA JUMLAH WISATAWAN NUSANTARA

The nonparametric regression approach is a statistical method used to determine the relationship between predictor variables and the dependent variable when the assumed pattern is unknown. Truncated spline is an estimator used in nonparametric regression to handle data with varying behaviors. Nonparametric regression modeling with truncated polynomial spline was applied to local Indonesian tourist visitation data obtained from BPS for the years 2017-2019, for each month. The optimal knot points were selected based on the smallest Gross Cross Validation values. Based on the analysis, the optimal model is a second-order spline with the smallest Gross Cross Validation value of 17,95 and the optimal knot points are in the 2nd, 6th, and 7th months. The goodness of the model is evident from an  value of 81,88% and an MSE of 12,46. The best model obtained shows a fairly accurate ability to explain the estimated number of domestic tourists so that it can be a basis for stakeholders to make key decisions in planning and managing the tourism industry as an effort to increase domestic tourism interest.

Precise Tensor Product Smoothing via Spectral Splines

Tensor product smoothers are frequently used to include interaction effects in multiple nonparametric regression models. Current implementations of tensor product smoothers either require using approximate penalties, such as those typically used in generalized additive models, or costly parameterizations, such as those used in smoothing spline analysis of variance models. In this paper, I propose a computationally efficient and theoretically precise approach for tensor product smoothing. Specifically, I propose a spectral representation of a univariate smoothing spline basis, and I develop an efficient approach for building tensor product smooths from marginal spectral spline representations. The developed theory suggests that current tensor product smoothing methods could be improved by incorporating the proposed tensor product spectral smoothers. Simulation results demonstrate that the proposed approach can outperform popular tensor product smoothing implementations, which supports the theoretical results developed in the paper.