Nonparametric Regression Research Articles

On the pitfalls of Gaussian likelihood scoring for causal discovery

Abstract We consider likelihood score-based methods for causal discovery in structural causal models. In particular, we focus on Gaussian scoring and analyze the effect of model misspecification in terms of non-Gaussian error distribution. We present a surprising negative result for Gaussian likelihood scoring in combination with nonparametric regression methods.

Semi-supervised inference for nonparametric logistic regression.

We consider the problem of estimating the nonparametric function in nonparametric logistic regression under semi-supervised framework, where a relatively small size labeled data set collected by case-control sampling and a relatively large size of unlabeled data containing only observations of predictors are available. This problem arises in various applications when the outcome variable is expensive or difficult to be observed directly. A two-stage nonparametric semi-supervised estimator based on spline method is proposed to estimate the target regression function by maximizing the likelihood function of the labeled case-control data. The unlabeled data are used in the first stage for estimating the density function that involves in the likelihood function. The consistency and functional asymptotic normality of the semi-supervised two-stage estimator are established under mild conditions. The proposed method, by making use of the unlabeled data, produces more efficient estimation of the target function than the traditional supervised counterpart. The performance of the proposed method is evaluated through extensive simulation studies. An application is illustrated with an analysis of a skin segmentation data.

A nonparametric instrumental approach to confounding in competing risks models.

This paper discusses nonparametric identification and estimation of the causal effect of a treatment in the presence of confounding, competing risks and random right-censoring. Our identification strategy is based on an instrumental variable. We show that the competing risks model generates a nonparametric quantile instrumental regression problem. Quantile treatment effects on the subdistribution function can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for which exact identification is possible and give partial identification results for other quantiles. We outline an estimation procedure and discuss its properties. The finite sample performance of the estimator is evaluated through simulations. We apply the proposed method to the Health Insurance Plan of Greater New York experiment.

Toward enhancing environmental quality in OECD countries: Role of municipal waste, renewable energy, environmental innovation, and environmental policy

The considerable increase in municipal waste has become a primary global concern due to the contamination of the environment through the emission of greenhouse gases. Therefore, many OECD countries have adopted municipal waste management practices. This study is a baseline attempt to explore the long-term effect of municipal waste management along with the energy transition, environmental innovation, and environmental policy stringency on GHG emissions in ten OECD countries from 1994 to 2020. This objective is realized by using non-parametric panel quantile regression. The estimated result reveals the asymmetric effect of selected explanatory variables on GHG emissions at various quantiles. The findings show that an increase in municipal waste can increase GHGs emissions at lower quantiles, while an insignificant effect is observed at higher quantiles. Similarly, energy transition, environmental innovation, and environmental policy stringency reveal asymmetric effects across the quantiles. The findings urge OECD countries to adopt more efficient municipal waste management practices and encourage renewable energy transition and environmental innovation. Environmental policy stringency can also be instrumental in enhancing environmental sustainability.

Convex support vector regression

Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least squares loss function often suffers from overfitting and outliers. This paper proposes to address these two issues by introducing the convex support vector regression (CSVR) method, which effectively combines the key elements of convex regression and support vector regression. Numerical experiments demonstrate the performance of CSVR in prediction accuracy and robustness that compares favorably with other state-of-the-art methods.

Environmental impact of globalization: The case of central and Eastern European emerging economies

Against the backdrop of piling environmental concerns in the modern era of globalization, this study aims to check the validity of the Pollution Haven Hypothesis (PHH) in Eastern European emerging countries and the relevance of globalization. The study targets to reduce the lack of consensus on the globalization-economic complexity-environment in European countries. Besides, we also intend to explore the existence of an N-shaped economic complexity-related Environmental Kuznets Curve (EKC) controlling for the bearing of renewable energy on environmental degradation. For analytical purposes, both parametric and non-parametric quantile regression approaches are employed. Overall, we find a non-linear relationship between economic complexity and carbon emissions, and N-shaped EKC is verified. Globalization and renewable energy consumption boost and inhibit emissions, respectively. More importantly, the results confirm the moderating role of economic complexity in neutralizing the carbon emissions-boosting effect of globalization.On the other hand, the non-parametric findings show that the N-shaped EKC hypothesis does not hold for high emissions quantiles. Furthermore, for all emissions quantiles, it is found that globalization boosts emissions, economic complexity, and globalization jointly curbs emissions and renewable energy curbs emissions. Based on the overall findings, some vital environmental development policies are recommended. The conclusions support shaping policy options promoting economic complexity and renewable energy as key factors in mitigating carbon emissions.

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.

Evaluating climatic change effects on EC and runoff in the near future (2020–2059) and far future (2060–2099) in arid and semi-arid watersheds

This study investigates the effect of climate change on the runoff and electrical conductivity (EC) of the Marun watershed. It used 35 general circulation models (GCMs) and the identification of unit hydrographs and component flows from rainfall, evaporation and streamflow data (IHACRES) rainfall-runoff model for the hydrological simulation. Moreover, a non-parametric regression model based on the multivariate adaptive regression splines (MARS) was utilized to estimate the EC under representative concentration pathway RCP4.5 and RCP8.5 scenarios in the near future F1 (2020–2059) and far future F2 (2060–2099) periods. Also, it used the technique for order of preference by similarity to ideal solution (TOPSIS) method to determine the best GCMs for each region and the k-nearest neighbors (KNN) technique to combine the temperature (Tmean) and precipitation (PCP) outputs and reduce the GCM uncertainty in each cell. According to the results, the highest increase of EC relative to the historical period (1966–2005) that will occur in the F1 period under the RCP4.5 and RCP8.5 scenarios is 17.43% and 15.6%, and for the F2 period is 18.46% and 11.2%, respectively, during autumn. The changes of annual Tmean, PCP, runoff, and EC in F1 period are 8.6%, 2.1%, − 10.7%, and − 11%, respectively, under the RCP4.5 scenario and 10.5%, 5.9%, − 3.5%, and − 12.2%, respectively, under the RCP8.5 scenario. The same values for the F2 period are 12.9%, − 0.1%, − 14.9%, and − 10%, respectively, under the RCP4.5 scenario and 22.6%, 5.2%, 1.2%, and − 12.8%, respectively, under the RCP8.5 scenario relative to the historical period.

A general result on complete f-moment convergence with its application to nonparametric regression models

In this paper, the complete f-moment convergence for weighted sums of sequences of extended negatively dependent random variables is investigated. As a result, we not only extend and generalize some results on complete convergence obtained by Wu and Zhai (Journal of Mathematical Inequalities, 13(1): 251-260, 2019), but also get some results on the complete consistency for the estimator of nonparametric regression models and provide some simulations to assess the validity of our theoretical results.

PERBANDINGAN MODEL ARIMA DENGAN MODEL NONPARAMETRIK POLINOMIAL LOKAL DAN SPLINE TRUNCATED UNTUK PERAMALAN HARGA MINYAK MENTAH WEST TEXAS INTERMEDIATE (WTI) DILENGKAPI GUI R

Crude oil as one of the most important natural resources experiences price fluctuations from time to time, even the spot price of West Texas Intermediate (WTI) world crude oil on 20th April 2020 reached -36,98 USD/barrel due to the Covid-19 pandemic. WTI oil price data was modeled using the ARIMA method, local polynomial, and spline truncated nonparametric regression then compared and obtained the best model and formed R Graphical User Interface (GUI). The ARIMA model and nonparametric time series models can be used to model time series data, but in the ARIMA model there are assumptions that must be fulfilled. Nonparametric time series models, which include local polynomial model and truncated spline do not need to fulfill these assumptions. The ARIMA model obtained did not fulfilled the assumptions of normality and residual homoscedasticity, so the modeling was stopped and modeling was only carried out using nonparametric regression methods. Based on the minimum MSE criteria, the best nonparametric model was obtained, namely nonparametric truncated spline model with degrees 3 and 3 knot points which was categorized as a strong model based on R-squared in sample value and having a very good forecasting ability based on MAPE out sample value.

PEMODELAN HARGA SAHAM PERUSAHAAN PROPERTI DAN REAL ESTATE MENGGUNAKAN REGRESI LONGITUDINAL SPLINE TRUNCATED DILENGKAPI GUI R

Stocks are one of the most popular financial instruments traded in the capital market. One of stock prices fluctuate up and down due to the influence of several factors, one of which is inflation. Stocks in the property and real estate sectors are important indicators to determine the level of a country economy. Data on several stock prices is one case of longitudinal data in economic field. The data is divided into 2 parts, namely in sample data from January 2016 to October 2020 and out sample data from November 2020 to December 2021. In this study, longitudinal stock price data is modeling using nonparametric spline truncated. The best spline truncated model is determined by the order and the optimal number of knot points based on the minimum Generalized Cross Validation value. Spline truncated nonparametric regression modeling for longitudinal data in this study is equipped with Graphical User Interface (GUI) that can facilitate the data processing. The results of the analysis show that the best longitudinal spline truncated regression model obtained on 2nd order with 5 knot points. 95.04% value of indicates the model is a strong model. In the evaluation of the best model, the MAPE data out sample value is 16.45%. It indicates the model has good forecasting ability.

Verbal memory formation across PET-based Braak stages of tau accumulation in Alzheimer's disease.

A classical early sign of typical Alzheimer's disease is memory decline, which has been linked to the aggregation of tau in the medial temporal lobe. Verbal delayed free recall and recognition tests have consistently probed useful to detect early memory decline, and there is substantial debate on how performance, particularly in recognition tests, is differentially affected through health and disease in older adults. Using in vivo PET-Braak staging, we investigated delayed recall and recognition memory dysfunction across the Alzheimer's disease spectrum. Our cross-sectional study included 144 cognitively unimpaired elderly, 39 amyloid-β+ individuals with mild cognitive impairment and 29 amyloid-β+ Alzheimer's disease patients from the Translational Biomarkers in Aging and Dementia cohort, who underwent [18F]MK6240 tau and [18F]AZD4694 amyloid PET imaging, structural MRI and memory assessments. We applied non-parametric comparisons, correlation analyses, regression models and voxel-wise analyses. In comparison with PET-Braak Stage 0, we found that reduced, but not clinically significant, delayed recall starts at PET-Braak Stage II (adjusted P < 0.0015), and that recognition (adjusted P = 0.011) displayed a significant decline starting at PET-Braak Stage IV. While performance in both delayed recall and recognition related to tau in nearly the same cortical areas, further analyses showed that delayed recall rendered stronger associations in areas of early tau accumulation, whereas recognition displayed stronger correlations in mostly posterior neocortical regions. Our results support the notion that delayed recall and recognition deficits are predominantly associated with tau load in allocortical and neocortical areas, respectively. Overall, delayed recall seems to be more dependent on the integrity of anterior medial temporal lobe structures, while recognition appears to be more affected by tau accumulation in cortices beyond medial temporal regions.

Prehospital Nursing Volunteer’s Personality Traits: A Motivational Perspective

Introduction:The aim of this cross-sectional, descriptive study was to determine the personality traits and motivation of nursing volunteers and their effects on pre-hospitalization emergency care.Method:Participants were 133 pre-hospital nursing volunteers from Taiwan. This study was performed using self-administered basic demographic information, Eysenck Personality Questionnaire-Revised Short (EPQ-RS), and Volunteer Motivation Scale with Chinese Volunteers (VMS-C). The statistical analysis was performed by SPSS 23.0. The data collections were analyzed by nonparametric statistics, correlation coefficient, covariance analysis, and one-way ANOVA analysis multiple regression analysis.Results:Our findings showed that having social desirability and extraversion personality had a positive impact on the attitudes of volunteers in terms of the provision of pre-hospital care. The first identified regulation was highlighted in the motivation scale; intrinsic motivation was secondarily emphasized. Pearson correlation coefficient revealed years of service in volunteering seniority, age, gender and nursing seniority were correlated. On the contrary, the job department and six municipalities were negatively correlated. Equivalence with the other relation, participants’ attending hours per month in volunteering and gender were positively related. Inverse correlations were found in age and nursing seniority. Extraversion personality and involvement in specific municipalities were positively correlated.Conclusion:Emergency Medical Services (EMS) has been developed in Taiwan for more than 20 years and must improve the quality of EMS. These results may be used to improve the quality of the pre-hospital care system and encourage nursing staff to join the system. Nursing volunteers in pre-hospital care are a particularly valuable resource, and satisfy a pivotal role early in the process of pre-hospital care. It is recommended that we provide a good interpersonal environment to maintain the good will of the dedicated, experienced, enthusiastic volunteers in Taiwan.

Evaluating semi- and nonparametric regression algorithms in quantifying stem taper and volume with alternative test data selection strategies

Abstract Accurately quantifying stem taper is essential to predict diameter at any given height along the stem and to estimate tree volume for various sections of the stem. With increased computing power, semi- and nonparamatric methods have been proposed as alternative approaches for modelling tree taper. The main objective of this study was to assess the accuracy of stem taper predicted for four pine and four hardwood species by semi- and nonparametric models. Specifically, generalized additive models (GAM), random forests (RF) and regression-enhanced random forests (RERF) were compared with two widely-used parametric models: variable-exponent function (VAR) and segmented polynomial regression model (SEG). Test datasets selected from four different data splitting methods were used to examine the prediction accuracy of the models. Results showed that all examined models can be used to quantify stem taper and volume for all species when prediction is limited to be within the range of tree sizes used in model building. The nonparametric RF algorithm generally produced higher bias and lower precision than the semiparametric (GAM and RERF) and parametric models (VAR and SEG). For all species, GAM, VAR and SEG provided more robust predictions of stem taper than RF and RERF algorithms, especially when small or large trees were withheld for model testing. The data splitting strategies used in this work provide an efficient ‘stress test’ to evaluate model performance when collecting an independent test dataset is not feasible. The findings of this work provide additional insights for forest practitioners and resource managers to select appropriate methods in stem taper modelling.

Minimax optimal regression over Sobolev spaces via Laplacian Eigenmaps on neighbourhood graphs

Abstract In this paper, we study the statistical properties of Principal Components Regression with Laplacian Eigenmaps (PCR-LE), a method for non-parametric regression based on Laplacian Eigenmaps (LE). PCR-LE works by projecting a vector of observed responses ${\textbf Y} = (Y_1,\ldots ,Y_n)$ onto a subspace spanned by certain eigenvectors of a neighbourhood graph Laplacian. We show that PCR-LE achieves minimax rates of convergence for random design regression over Sobolev spaces. Under sufficient smoothness conditions on the design density $p$, PCR-LE achieves the optimal rates for both estimation (where the optimal rate in squared $L^2$ norm is known to be $n^{-2s/(2s + d)}$) and goodness-of-fit testing ($n^{-4s/(4s + d)}$). We also consider the situation where the design is supported on a manifold of small intrinsic dimension $m$, and give upper bounds establishing that PCR-LE achieves the faster minimax estimation ($n^{-2s/(2s + m)}$) and testing ($n^{-4s/(4s + m)}$) rates of convergence. Interestingly, these rates are almost always much faster than the known rates of convergence of graph Laplacian eigenvectors to their population-level limits; in other words, for this problem regression with estimated features appears to be much easier, statistically speaking, than estimating the features itself. We support these theoretical results with empirical evidence.

A model for damage and failure of carbon-carbon composites: development and identification through Gaussian process regression

The paper presents a model for damage accumulation and failure of carbon-carbon (C/C) thick laminates used in automotive disc brakes, with 2.5D reinforcement and disordered lamination sequences. The highly non-linear response of laminates in different stress states was acquired through tensile and Double Cantilever Beam tests performed on specimens cut from discs. The paper adopts a novel bi-phasic approach based on Cohesive Zone Model to model delamination, matrix cracking and fibres failure to predict the structural integrity of laminates. Since the non-homogeneous lay-ups required a robust identification tool for the material properties, modern automatic techniques were used, such as genetic optimization and non-parametric Gaussian process regression, to identify the material model parameters both in the elastic and inelastic ranges. Considering all the tests, the qualitive and quantitative correlation that was achieved indicates that the constitutive law adopted adequately represents the physical damage mechanisms of the C/C material in severe load conditions and that the identification methods adopted represent effective tools to calibrate complex material models for the prediction of the strength and damage tolerance of C/C and, in general, composite laminates.

APPLICATION OF PANELIZED SPLINE-SPATIAL AUTOREGRESSIVE MODEL TO HIV CASE DATA IN INDONESIA

Spatial regression analysis is a statistical method used to perform modeling by considering spatial effects. Spatial models generally use a parametric approach by assuming a linear relationship between explanatory and response variables. The nonparametric regression method is better suited for data with a nonlinear connection because it does not need linear assumptions. One of the nonparametric regression methods is penalized spline regression (P-Spline). The P-spline has a simple mathematical relationship with mixed linear model. The use of a mixed linear model allows the P-Spline to be combined with other statistical models. PS-SAR is a combination of the P-Spline and the SAR spatial model so that it can analyze spatial data with a semiparametric approach. Based on data from monitoring the development of the HIV situation in 2018, the number of HIV cases in Indonesia shows a clustered pattern that indicate spatial dependence. In addition, the relationship between the number of positive cases and the factors tends to be nonlinear. Therefore, this study aims to apply the PS-SAR model to HIV case data in Indonesia. The resulting model is evaluated based on the estimates of autoregressive spatial coefficient, MSE, MAPE, and Pseudo R2. Based on the results, the PS-SAR model has an autoregressive spatial coefficient similar to the SAR model and has smaller MSE and MAPE than the SAR model.

Non-parametric, semi-parametric, and machine learning models for river temperature frequency analysis at ungauged basins

River water temperature is essential in regulating many physical and biochemical processes in river systems. Consequently, it is crucial to develop reliable tools for predicting extreme river temperatures at sites with little or no available data. This study aims to compare two machine learning models, random forest (RF) and extreme gradient boosting (XGBoost), with non-parametric multivariate adaptive regression splines (MARS) and semi-parametric generalized additive models (GAMs) for the regional estimation of maximum water temperatures at ungauged locations. Three linear and non-linear approaches are also considered in the homogeneous regions delineation step of regional frequency analysis: canonical correlation analysis (CCA), neural network-based canonical correlation analysis (NLCCA), as well as considering all stations (ALL). The results indicate that GAM and MARS lead to the best performances. The performance of NLCCA+GAM is the best in terms of absolute and relative mean square error, followed by CCA + MARS. A significant improvement in the performance of adopted models is achieved by using neighborhood methods. The two machine learning models are tested using two variable selection methods: Recursive Feature Elimination (RFE) and Least Absolute Shrinkage and Selection Operator (LASSO). The results, however, do not show any significant differences. These results may be indicative of the flexibility and ability of the GAM and MARS approaches to reproduce thermal extremes, especially under real-world conditions when a limited amount of data is available.

REGRESSION NONPARAMETRIC SPLINE ESTIMATION ON BLOOD GLUCOSE OF INPATIENTS DIABETES MELLITUS AT SAMARINDA HOSPITAL

This study used a biresponse nonparametric regression method with truncated spline estimation that used two response variables. Nonparametric regression method is used when the regression curve is not known for its shape and pattern.One of the nonparametric regression model approaches that is often used is the spline. The truncated spline approach has a segmented polynomial function that provides flexibility. The data used in the study were blood glucose levels in patients with diabetes mellitus, cholesterol levels, and triglyceride levels in 2020. From the results of the study, the best nonparametric biresponse spline truncated regression model with three knot points has been obtained where the minimum GCV value is and has the an value of .

Non-Parametric Regression and Riesz Estimators

In this paper, we consider a non-parametric regression model relying on Riesz estimators. This linear regression model is similar to the usual linear regression model since they both rely on projection operators. We indicate that Riesz estimator regression relies on the positive basis elements of the finite-dimensional sub-lattice generated by the rows of some design matrix. A strong motivation for using the Riesz estimator model is that the data of explanatory variables may come from categorical variables. Calculations related to Riesz estimator regression are very easy since they arise from the measurability in finite-dimensional probability spaces. Moreover, we show that the fitted model of Riesz estimators is an ordinary least squares model. Any vector of some Euclidean space is supposed to be a rendom variable under the objective probability values, being used in expected utility theory and its applications. Finally, the reader may notice that goodness-of-fit measures are similar to those defined for the usual linear regression. Due to the fact that this model is non-parametric, it may include samples relevant to finance and actuarial science variables.