Nonparametric Additive Regression Research Articles

Nonparametric Additive Regression for High-Dimensional Group Testing Data

Group testing has been verified as a cost-effective and time-efficient approach, where the individual samples are pooled with a predefined group size for subsequent testing. Recent research has explored the integration of covariate information to improve the modeling of the group testing data. While existing works for high-dimensional data primarily focus on parametric models, this study considers a more flexible generalized nonparametric additive model. Nonlinear components are approximated using B-splines and model estimation under the sparsity assumption is derived employing group lasso. Theoretical results demonstrate that our method selects the true model with a high probability and provides consistent estimates. Numerical studies are conducted to illustrate the good performance of our proposed method, using both simulated and real data.

Wavelet estimation for the nonparametric additive model in random design and long-memory dependent errors

We investigate the nonparametric additive regression estimation in random design and long-memory errors and construct adaptive thresholding estimators based on wavelet series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function and its univariate additive components belong to Besov space. We consider the problem under two noise structures; (1) homoskedastic Gaussian long memory errors and (2) heteroskedastic Gaussian long memory errors. In the homoskedastic long-memory error case, the estimator is completely adaptive with respect to the long-memory parameter. In the heteroskedastic long-memory case, the estimator may not be adaptive with respect to the long-memory parameter unless the heteroskedasticity is of polynomial form. In either case, the convergence rates depend on the long-memory parameter only when long-memory is strong enough, otherwise, the rates are identical to those under i.i.d. errors. In addition, convergence rates are free from the curse of dimensionality.

Financial decentralization, renewable energy technologies, energy subsidies and wind power development in China: An analysis of nonparametric model

Currently, financial development and renewable energy technologies have become new tools to stimulate wind power development, attracting attention from the government and academia. However, most existing literature uses linear methods to investigate wind power, masking the nonlinear relationship between these factors and wind power development. The objective of this study is to reveal the nonlinear relationships between these economic factors and wind power development, providing a basis for the government to design differentiated phased policies. Compared to traditional linear methods, the nonparametric models can truly simulate the nonlinear relationship between these economic factors and wind power development. Given this, this article uses the nonparametric additive regression model to investigate these links. The result of this study shows: (1) financial decentralization produces a U-shaped impact on wind power, indicating that expanding the autonomy of local financial institutions has driven wind power development in the later stage. (2) The impact of renewable energy technologies demonstrates an inverted U-shaped pattern, signifying that the driving effect of green technology has shifted from being prominent in the early stage to being reduced in the later stage. (3) Energy subsidies also exert an inverted U-shaped effect, meaning that its driving role is prominent in the early stage. (4) In addition, the impacts of CO2 emissions, wind power prices, environmental governance investments, and urbanization on wind power development also exhibit non-linear characteristics. Finally, this article proposes policies in response to the stage where economic tools don't play a role in driving wind power development.

Macro Stress Testing the Credit Risk of Conventional and Participation Banks in Turkey: A Nonparametric Quantile Regression Approach

ABSTRACT This paper applies a novel time series-based additive nonparametric quantile regression technique to stress test the credit risk of conventional and participation banks in Turkey. We particularly examine the effects of the exchange rate, unemployment rate, the policy interest rate, and the public debt-to-GDP ratio on the non-performing loan ratio (NPL) of Turkish banks at distinct quantile levels. We find that their effects are heterogeneous and significantly vary across different types of banks and quantiles. Overall, participation banks are more vulnerable to negative scenarios associated with the exchange rate, unemployment rate, and public debt ratio than conventional banks.

Identifying important gene signatures of BMI using network structure-aided nonparametric quantile regression.

We focus on identifying genomics risk factors of higher body mass index (BMI) incorporating a priori information, such as biological pathways. However, the commonly used methods to incorporate prior information provide a model for the mean function of the outcome and rely on unmet assumptions. To address these concerns, we propose a method for nonparametric additive quantile regression with network regularization to incorporate the information encoded by known networks. To account for nonlinear associations, we approximate the unknown additive functional effect of each predictor with the expansion of a B-spline basis. We implement the group Lasso penalty to obtain a sparse model. We define the network-constrained penalty by the total norm of the difference between the effect functions of any two linked genes in the known network. We further propose an efficient computation procedure to solve the optimization problem that arises in our model. Simulation studies show that our proposed method performs well in identifying more truly associated genes and less falsely associated genes than alternative approaches. We apply the proposed method to analyze the microarray gene-expression dataset in the Framingham Heart Study and identify several 75 percentile BMI associated genes. In conclusion, our proposed approach efficiently identifies the outcome-associated variables in a nonparametric additive quantile regression framework by leveraging known network information.

Solar energy investment, technological innovation and carbon emission reduction: Evidence from China

The aim of this paper is to investigate the impact of solar energy investment on carbon emissions. The STIRPAT model, a non-parametric additive regression model, and the vector autoregression model are built to investigate the comprehensive effect of solar energy investment on China’s carbon emissions. Solar energy investment and other factors related to carbon emissions are examined. The empirical study shows that it will take about 8 years for the solar energy investment to promote carbon emission reductions. The moderation analysis indicates that technological innovation has a moderating effect in the facilitation of carbon emission reduction by solar energy investment. The finding of this study has some meaningful policy implications. In order to achieve the goal of carbon emission reduction, China should keep solar energy investment continuous and steady and improve technological innovation.

The effects of structural and technical change on China’s industrial CO2 emissions pathways under uncertainty

ABSTRACT The industrialization process in China has resulted in the fast growth of the country’s energy consumption and CO2 emissions. Examining the effects of industrial structural change on the emissions pathways in the mid-term future would help advance understanding of how industrial policy choices affect the fulfillment of the strategic climate targets of emissions peaking and carbon neutrality. This study couples index decomposition analysis (IDA) with an additive nonparametric regression model to project the possible emissions pathways with different industrial structures. It develops a set of scenarios following the storylines of shared socioeconomic pathways (SSPs) to examine these effects in an uncertain environment towards 2040. The results show that structural change has played an increasing role in curbing carbon emissions of China’s industrial sectors since 2000. The CO2 emissions reductions attributable to this effect were 686 million tons (Mton CO2) between 2000 and 2013, and these contributions to emission mitigation rose to 798 Mton between 2014 and 2019. The scenario results suggest that the aggregated effect of energy efficiency and structure upgrades will decrease emissions by 43% in 2040 relative to the level in 2019 in the ideal case. Regardless of the uncertainties in scenario settings, heavy industry will continue to dominate China’s industrial emissions through 2040. Nevertheless, a significant structural change with an increased share of high-tech industries, such as information and communication technology, could lead to more than a 30% reduction in emissions compared to cases with more minor changes in this sub-sector. Key Policy Insights A rapid expansion of heavy industry is the primary factor driving the rapid growth of China’s industrial CO2 emissions since 2000. Industrial structural change is the second most significant factor curbing emissions growth, and the influence of this factor is increasing. Keeping up the momentum of structural change and technological upgrades in the industrial sector would make it possible for industry emissions to decrease in the medium-term future, therefore contributing substantially to China’s goal of peaking its CO2 emissions by 2030. Realizing carbon neutrality in the longer term necessitates not only structural change in industry, but also a fundamental transformation of the energy supply system.

Greenhouse gas emissions and its driving forces in the transport sector of South Africa

The reliance on energy to power vehicles in the transport sector is solely fossil-based fuels. These are the dominant source of greenhouse gas emissions (GHGs) posing huge threats to climate change and increasing global warming. To detect the driving forces responsible for GHG emissions in realising its intensity target, the paper examines the national population, economic growth, energy intensity, urbanisation, infrastructural investments, fuel consumption, freight turnover and passenger vehicles on energy related GHGs emissions in the South Africa’s transport sector from 2011 to 2020 by applying an extended Stochastic Impact by Regression on Population, Affluence and Technology (STIRPAT) and nonparametric additive regression to assess the main driving forces. The empirical results revealed that increase in population, economic growth, energy intensity, passenger vehicles and freight transport are more liable to cause an increase in GHG emissions. From the estimated elastic coefficient, the study shows that population and economic growth are the most influencing factors to GHGs emitted. Others are also significant but more often dependent on the increasing population and the nation’s economic growth. Hence, for policy recommendations in mitigating GHG emissions the dynamic effects of the influencing factors at varying provinces and periods should be of consideration in mitigating GHG emissions in the transportation sector of South Africa.

Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods

<p class='IJASEITAbtract'>Nowadays, most nonparametric regression research involves more than one predictor variable and generally uses the same type of estimator for all predictors. In the real case, each predictor variable likely has a different form of regression curve so that if it is forced, it can produce an estimation form that does not match the data pattern. Thus, it is necessary to develop a regression curve estimation model under the data pattern, namely the mixed estimator. The focus of this study is an additive nonparametric regression model, a mix of the Truncated Spline and Gaussian Kernel. There is a knot point in the Truncated Spline, while in the Gaussian Kernel, there is bandwidth. To choose the optimal knot point and bandwidth in a mixed estimator model, various methods can be used, including Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). This research proposes the optimal knot point and bandwidth estimation on the mixed estimator Truncated Spline and Gaussian Kernel model. Furthermore, the comparison between CV, GCV, and UBR is used to validate the proposed method. The simulation study was carried out by generating the Truncated Spline function and the Gaussian Kernel on a combination of sample size variations and variances. The simulation results show that the GCV method provides a higher coefficient of determination (R²) value and better accuracy for each combination of sample sizes and variance variations.

A non-parametric analysis of the driving factors of China's carbon prices

Carbon prices have gradually become the principal policy for controlling carbon dioxide emissions, which has attracted the attention of countries worldwide. The price factor is significantly affected by the market economy and often exhibits non-linear characteristics. This article aims to investigate the possible non-linear relationship between carbon prices and their influencing factors using a data-driven non-parametric additive regression model. Estimated results show that coal prices have an inverted U-shaped non-linear impact on carbon prices. It means that coal prices pushed up carbon prices; in the long run, the changes in coal prices will help reduce carbon prices. The real economy also exerts an inverted U-shaped effect on carbon prices, which is the main reason for the rapid expansion of energy-intensive industries in the short run. The impact of natural gas prices presents a gentle inverted U-shaped pattern, owing to the periodic changes in natural gas consumption. On the contrary, renewable energy prices have a “lower first, then increase” U-shaped impact on carbon prices. Therefore, the government should formulate differentiated policies at different time stages.

PLA-Cu reinforced composite filament: preparation and flexural property printed at different machining conditions

Fused Deposition Modeling (FDM) is commonly used to construct complicated design, especially for medical applications. In the present work, 12 rate weight percentage of copper powder with a molecule size of 30–50 µm is used in the Poly Lactic Acid (PLA) matrix as a fortification to form a composite fiber. For the variable working conditions, the samples are printed to ASTM D-790. In FDM, layer height, bed temperature, and nozzle temperature are taken as variable parameters to measure the bending property. The Scanning Electron Microscope (SEM) and 3-dimensional optical pictures examine the flexural quality, crack mechanics, and impact of various printed conditions for three-point flexural tests. A layer thickness of 0.14 mm was recorded for the maximum flexural quality of 68.6 MPa. The fracture mechanism is considered as identical under any machining conditions. Layer height predominantly determines the material’s flexural property and the uniform dispersion of the copper molecule over the crack surface which is confirmed by surface topography. Also, the non-parametric Bayesian Additive Regression Trees (BART) model is created to benefit from the earlier use of this inferential structure to measure vulnerability and information alignment.

Impact of renewable energy investment on carbon emissions in China - An empirical study using a nonparametric additive regression model

This study analyzed the comprehensive impact of renewable energy investment on carbon emissions in China. To achieve this, a nonparametric additive regression model was built. Using the STIRPAT model, we considered six influencing factors: economic growth, industrialization level, urbanization level, population aging, trade openness, and renewable energy investment. This enabled the exploration of the existence, direction, and intensity of the impact of renewable energy investment on carbon emissions. The results of the linear component of the model showed that renewable energy investment can slightly reduce carbon emissions. The results of the nonlinear component of the model showed that the impacts of renewable energy investment on carbon emissions were inconsistent at different stages of the investment. In the early stage, the renewable energy investment can increase carbon emissions. In the middle stage, the renewable energy investment begins to play a role in reducing emissions. In the later stage, renewable energy investment may be associated with increased carbon emissions again. The relationship between carbon emissions and the other five influencing factors can be represented by an inverted U-shaped curve, a U-shaped curve, or a slow rising curve. The results above provide useful references to adjust renewable energy investment and reduce carbon emissions.

How to achieve a low-carbon transition in the heavy industry? A nonlinear perspective

The heavy industry is the main source of CO2 emissions. Examining the influencing factors of the heavy industry's CO2 emissions is essential for this industry to achieve a low-carbon transition. Existing research literature often assumes that the relationship between the influencing factors and CO2 emissions is linear. In fact, most economic phenomena are characterized by fluctuations, due to the influence of business cycles. This often leads to more likely nonlinear relationships between economic variables. This paper uses nonparametric additive regression model to investigate CO2 emissions from China's heavy industry. The empirical findings show that economic growth, urbanization, and energy efficiency exert a “first promotion, then restriction” inverted “U-shaped” nonlinear effect on CO2 emissions. To complicate matters further, energy consumption structure and export dependence have an “N-shaped” nonlinear effect on CO2 emissions. Therefore, in the early stage, the government should actively optimize the industrial structure, strengthen the management of the real estate industry, and expand R&D investment. In the long run, the government should subsidize the heavy industry to expand clean energy consumption, and provide tax incentives to support the export of high-tech industrial products.

Assessment of integrative non-pharmacological interventions and quality of life in breast cancer patients using real-world data.

Treatments with non-pharmacological interventions (NPIs), comprising art and exercise therapies, nursing interventions, and educational components, are considered to improve quality of life of cancer patients. The aim of this study was to assess the longitudinal changes in self-reported quality of life of breast cancer patients receiving an integrative medicine program consisting of hospital-based NPIs and standard oncological treatments. This real-world data study was conducted using data from the Network Oncology clinical registry of the Gemeinschaftskrankenhaus Havelhöhe. Primary breast cancer patients of all tumor stages, who answered the European Organization of Research and Treatment Health-Related Quality of Life Core Questionnaire scale (EORTC QLQ-C30) at first diagnosis and 12months later, were included. Association factors between received NPIs and longitudinal EORTC QLQ-C30-changes were analyzed with additive non-parametric regression tests, considering treatment regimens and demographic variables, using the software R. A total of 231 primary breast cancer patients were enrolled and separate regression analyses were carried out. Significant associations between the received NPIs elaborate consultations and life review, nursing compresses, music and eurythmy therapy and improvements of 8-13 points for global health, all five functional EORTC-scales, and symptoms fatigue, dyspnea, insomnia, and financial difficulties were observed. Our findings support the beneficial impact of NPIs for breast cancer patients. Further research could be directed towards synergistic effects of multimodal applied NPIs. Trial registration number DRKS00013335 on 27/11/2017 retrospectively registered.

Additive regression for predictors of various natures and possibly incomplete Hilbertian responses

In this paper we consider a fully nonparametric additive regression model for responses and predictors of various natures. This includes the case of Hilbertian and incomplete (like censored or missing) responses, and continuous, nominal discrete and ordinal discrete predictors. We propose a backfitting technique that estimates this additive model, and establish the existence of the estimator and the convergence of the associated backfitting algorithm under minimal conditions. We also develop a general asymptotic theory for the estimator such as the rates of convergence and asymptotic distribution. We verify the practical performance of the proposed estimator in a simulation study. We also apply the method to various real data sets, including those for a density-valued response regressed on a mixture of continuous and nominal discrete predictors, for a compositional response regressed on a mixture of continuous and ordinal discrete predictors, and for a censored scalar response regressed on a mixture of continuous and nominal discrete predictors.

How to efficiently promote distributed energy resources in China: Using a nonparametric econometric method

Most of the existing related studies use linear methods to investigate distributed energy resources, ignoring the objectively existing nonlinear relationships. This article makes improvement and uses a nonparametric additive regression model to explore China’s distributed energy resources. Estimated results show that technological progress exerts an inverted “U-shaped” nonlinear effect on distributed energy resources, due to the phased changes in R&D expenditures. Energy consumption structure also has an inverted U-shaped impact, which main reason is the changes in natural gas and renewable energy consumption. On the contrary, international oil prices have a positive U-shaped impact on distributed energy resources, because international oil prices are gradually increasing over time. Foreign oil dependence has an N-shaped nonlinear impact, which is mainly due to the changes in oil imports at different stages. The relationship between urbanization and distributed energy resources also presents an N-shaped pattern. This is mainly due to the periodic changes in the growth rate of the number of residents using natural gas. The research results can provide empirical support for the government to formulate targeted distributed energy policies at different stages.

Empirical Bayes oracle uncertainty quantification for regression

We propose an empirical Bayes method for high-dimensional linear regression models. Following an oracle approach that quantifies the error locally for each possible value of the parameter, we show that an empirical Bayes posterior contracts at the optimal rate at all parameters and leads to uniform size-optimal credible balls with guaranteed coverage under an “excessive bias restriction” condition. This condition gives rise to a new slicing of the entire space that is suitable for ensuring uniformity in uncertainty quantification. The obtained results immediately lead to optimal contraction and coverage properties for many conceivable classes simultaneously. The results are also extended to high-dimensional additive nonparametric regression models.

Impact of natural gas consumption on sub-Saharan Africa's CO2 emissions: Evidence and policy perspective

With huge natural gas(NG) reserves and current low (1%) share of non-hydro renewables in Sub-Saharan Africa (SSA), can natural gas offer SSA a low-carbon energy transition? Employing data from 1980 to 2017, this paper investigates the impact of NG consumption on SSA's CO2 emissions using data-driven nonparametric additive regression(NPAR) which can reveal both linear and nonlinear effects. Augmenting NPAR with translog production function(TPF) estimates of interfuel substitution elasticities and bias technological progress over sample period(advantage of TPF), we further provide evidence of the indirect effect of NG consumption on SSA's CO2 emissions through mechanism analysis. From the empirical results, the linear effect shows NG positively impact CO2 emissions while the nonlinear effect indicates a downward decreasing trend (meaning expansion in NG consumption will gradually lower CO2 emissions). Nonlinearly, urbanization and energy efficiency also show positive “inverted U-Shaped” and “downward slopping” respectively meaning sustainable urban energy and energy efficiency practices improvement can lead to CO2 reduction respectively in SSA. The reducing effect of NG consumption on CO2 (the nonlinear effect) is realized through the enhancement of positive bias technological progress of NG over coal and oil but not merely substitution of coal and oil for NG. Technological progress improvement in NG use will also reduce the positive linear effect of urbanization and energy efficiency on CO2 emissions of SSA. Oil is more likely to be substituted for NG than that of coal in SSA. The scenario analysis shows a total of 6.9%, 7.6% and 8.3% of energy conservation is realized in 2022, 2026 and 2030 with a corresponding CO2 reduction of 18.7%, 20.7% and 22.9% respectively for a continuous 10% investment in NG. Institutional, market-oriented and technology challenges hinder NG development among major producers in SSA. Based on the results, several policy measures are put forward to promote SSA's low-carbon energy transition.

How to achieve green growth in China’s agricultural sector

Green development is the direction of China’s agricultural sector. Investigating the main influencing factors of the agricultural sector’s CO2 emissions will help plan agricultural development and achieve low-carbon growth. This paper selects 2001–2016 panel data of China’s 30 provinces, and uses the nonparametric additive regression models to investigate the agricultural sector’s CO2 emissions. The empirical results show that economic growth, financial capacity, and energy intensity all have a “pull first, then restrict” inverted U-shaped nonlinear effect on CO2 emissions. However, the influencing mechanisms of these three influencing factors are different and need to be paid attention by relevant government departments. More complicated, the impact of urbanization on CO2 emission shows a gentle “M-shaped” pattern. In addition, an inverse “N-shaped” nonlinear link exists between trade openness and CO2 emissions. Therefore, government departments should formulate differentiated emission reduction policies at different stages.

How does fossil energy abundance affect China's economic growth and CO2 emissions?

The paper uses the nonparametric additive regression model with data- driven characteristics to investigate the impact of fossil energy abundance on China's economic growth and carbon dioxide (CO2) emissions. The results show that the effect of fossil energy abundance on economic growth shows an inverted “U-shaped” pattern in the eastern region, due to the changes in coal mining, oil processing, and coking investments. On the contrary, fossil energy abundance exerts a positive “U-shaped” nonlinear effect on economic growth in the central region. This indicates that in the early stages fossil energy abundance did not play a role in promoting economic growth, and its driving effect was only prominent in the later stages. In addition, fossil energy abundance generates a positive “U-shaped” impact on CO2 emissions in the eastern and central regions, because of the changes in coal and oil consumption at different stages. However, fossil energy abundance has an inverted “U-shaped” nonlinear effect on CO2 emissions in the western region, on account of the phase difference in the production and consumption of natural gas and oil.