Nonparametric Additive Regression Model Research Articles

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.

A one-covariate-at-a-time multiple testing approach to variable selection in additive models

. This article proposes a One-Covariate-at-a-time Multiple Testing (OCMT) approach to choose significant variables in high-dimensional nonparametric additive regression models. Similarly to Chudik, Kapetanios, and Pesaran, we consider the statistical significance of individual nonparametric additive components one at a time and take into account the multiple testing nature of the problem. Both one-stage and multiple-stage procedures are considered. The former works well in terms of the true positive rate only if the net effects of all signals are strong enough; the latter helps to pick up hidden signals that have weak net effects. Simulations demonstrate the good finite-sample performance of the proposed procedures. As an empirical illustration, we apply the OCMT procedure to a dataset extracted from the Longitudinal Survey on Rural Urban Migration in China. We find that our procedure works well in terms of out-of-sample root mean square forecast errors, compared with competing methods such as adaptive group Lasso (AGLASSO).

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.

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.

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.

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.

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.

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.

Albemarle reports 2Q 2019 growth and raises full year EPS guidance

The bulk commodities are basic goods, and their price fluctuations are directly related to the stability of a country's macro economy. Investigating the main driving forces of the commodity price fluctuations is the key to stabilizing the macro economy. Ignoring the objective facts that there are a large number of nonlinear relationships between economic variables, most of the existing scholars use the linear models to commodity price fluctuations. To compensate for the shortcomings of existing research, this paper uses the nonparametric additive regression model with data-driven features to investigate the main driving forces of China’s commodity price fluctuations. The results show that exchange rate has an “early promotion, late inhibition” inverse “U-shaped” nonlinear effect on commodity price fluctuations because the renminbi appreciates in the early stages, but depreciates in the later stages. The nonlinear impact of the real economy also appears an inverted “U-shaped” pattern, due to the changes in growth mode of the real economy. Similarly, international oil price produces an inverted “U-shaped” nonlinear effect, owing to the rise in international oil prices in the early stages and the decline in the later stages. However, the money supply has an “early inhibition, late promotion” positive “U-shaped” nonlinear effect on commodity prices. Therefore, government departments should formulate targeted policies over time to effectively stabilize China’s commodity prices.

How to effectively stabilize China's commodity price fluctuations?

The bulk commodities are basic goods, and their price fluctuations are directly related to the stability of a country's macro economy. Investigating the main driving forces of the commodity price fluctuations is the key to stabilizing the macro economy. Ignoring the objective facts that there are a large number of nonlinear relationships between economic variables, most of the existing scholars use the linear models to commodity price fluctuations. To compensate for the shortcomings of existing research, this paper uses the nonparametric additive regression model with data-driven features to investigate the main driving forces of China’s commodity price fluctuations. The results show that exchange rate has an “early promotion, late inhibition” inverse “U-shaped” nonlinear effect on commodity price fluctuations because the renminbi appreciates in the early stages, but depreciates in the later stages. The nonlinear impact of the real economy also appears an inverted “U-shaped” pattern, due to the changes in growth mode of the real economy. Similarly, international oil price produces an inverted “U-shaped” nonlinear effect, owing to the rise in international oil prices in the early stages and the decline in the later stages. However, the money supply has an “early inhibition, late promotion” positive “U-shaped” nonlinear effect on commodity prices. Therefore, government departments should formulate targeted policies over time to effectively stabilize China’s commodity prices.

Can expanding natural gas consumption reduce China's CO2 emissions?

China is now the world's largest emitter of carbon dioxide (CO2), thus leading to China facing enormous pressure on CO2 emission reduction. Natural gas is a high thermal and low-emission energy. Expanding natural gas consumption cannot only meet the growing demand for energy consumption but also optimize energy consumption structure. Therefore, many scholars have investigated the effect of natural gas consumption on CO2 emissions. However, ignoring a large number of nonlinear relationships between economic variables, the vast majority of existing studies use traditional linear models to explore the relationships between natural gas consumption and CO2 emissions. In order to make up for the gap in existing research, this paper uses the nonparametric additive regression model with data-driven features to investigate the relationships between the two. The results show that natural gas consumption has an inverted “U-shaped” nonlinear effect on CO2 emissions in the eastern region, but a positive “U-shaped” nonlinear effect in the central and western regions. The linear impact of natural gas consumption on CO2 emissions in the eastern and central regions is higher than that in the western region, due to the differences in resource availability and energy prices, as well as natural gas consumption. Therefore, during the process of promoting natural gas consumption, the central and local governments should adopt heterogeneous measures at different stages of development.

Influencing factors of the carbon dioxide emissions in China's commercial department: A non-parametric additive regression model

The commercial department plays a significant role in China's energy conservation and carbon dioxide emission mitigation. The study employs a panel data set during 2001–2015 and adopts a non-parametric additive regression model to analyse the drivers of commercial department's carbon dioxide emissions in China. Non-parametric additive regression model based on the provincial panel data is first applied to investigate the carbon dioxide emissions in China's commercial department. The consequences demonstrate that the nonlinear impact of economic growth upon carbon dioxide emissions is in accordance with the Environmental Kuznets Curve (EKC) hypothesis. Energy intensity is currently in the left half of the “overturned U-shaped” relationship. In the long run, the overturned “U-shaped” impact of energy intensity may be due to the discrepant level of technological development in different phases. Nevertheless, the urbanization demonstrates an erected “U-shaped” impact on carbon dioxide emissions owing to the further urban commercial consumption and fixed asset investment in recent times. Aggregate population presents a fast-to-slow growth relationship, which is the result that residents require massive commercial goods with the augment in population and income. Energy structure also reveals an erected “U-shape” relationship on account of slight electricity consumption in former times and the large amount of thermal power consumption in later phases. As a result, we should take into full consideration the disparate fluctuant impacts of these influencing indicators when it comes to carbon dioxide emissions in commercial department.

Estimating nonlinear additive models with nonstationarities and correlated errors

AbstractIn this paper, we study a nonparametric additive regression model suitable for a wide range of time series applications. Our model includes a periodic component, a deterministic time trend, various component functions of stochastic explanatory variables, and an AR(p) error process that accounts for serial correlation in the regression error. We propose an estimation procedure for the nonparametric component functions and the parameters of the error process based on smooth backfitting and quasimaximum likelihood methods. Our theory establishes convergence rates and the asymptotic normality of our estimators. Moreover, we are able to derive an oracle‐type result for the estimators of the AR parameters: Under fairly mild conditions, the limiting distribution of our parameter estimators is the same as when the nonparametric component functions are known. Finally, we illustrate our estimation procedure by applying it to a sample of climate and ozone data collected on the Antarctic Peninsula.

Nonparametric additive beta regression for fractional response with application to body fat data

Fractional data that are restricted in the standard unit interval (0, 1) with a highly skewed distribution are commonly encountered. Such data arise in various areas, such as economics, finance, and medicine, among others. One natural idea to model such data is to use the beta family due to its flexibility to accommodate various density shapes. In this paper, we propose a nonparametric additive beta regression model along with a variable selection procedure, where the mean response is related to covariates through the combination of unknown functions of covariates, which can be approximated on a B-spline basis. By using this approximation method, we transform the problem of variable selection into the problem of selecting the groups of coefficients in the expansion. Based on the penalized likelihood method for group variable selection, we successfully select the significant covariates. Moreover, the estimation and selection consistencies and the properties of the penalized estimators are established. The simulation studies demonstrate that the performance of our proposed method is quite good. Finally, we apply the proposed method to body fat data, and we obtain several important findings with satisfactory selection and prediction performance.

Assessing the development of China's new energy industry

As the world's largest carbon dioxide (CO2) emitter, China is facing increasing international pressure to reduce emissions. Actively developing new energy has become a fundamental means to solve the dilemma between environmental pollution and energy consumption growth. Thus, more scholars have conducted a wide range of studies on the new energy industry. However, most of the existing studies use traditional linear models to investigate the relationships between new energy industry and its driving forces, ignoring the objective reality that there are many nonlinear relationships in economic variables. In order to overcome the shortcomings of existing research, this paper uses a data-driven nonparametric additive regression model to study the new energy industry. The results show that the nonlinear effect of agricultural development shows an inverted “U-shaped” pattern due to the changes in crop acreage at different stages of development. The nonlinear impact of foreign energy dependence also indicates an inverted “U–shaped” pattern. However, technological progress produces a positive “U–shaped” nonlinear impact on the new energy industry because of the difference in R&D funding and R&D personnel investments. Similarly, the impact of energy consumption structure also shows a positive “U–shaped” pattern, owing to the gradual decline in coal consumption. Therefore, the government should develop differentiated policies at different stages, in order to effectively promote the development of new energy industries.

Does the high–tech industry consistently reduce CO2 emissions? Results from nonparametric additive regression model

China is currently the world's largest carbon dioxide (CO2) emitter. Moreover, total energy consumption and CO2 emissions in China will continue to increase due to the rapid growth of industrialization and urbanization. Therefore, vigorously developing the high–tech industry becomes an inevitable choice to reduce CO2 emissions at the moment or in the future. However, ignoring the existing nonlinear links between economic variables, most scholars use traditional linear models to explore the impact of the high–tech industry on CO2 emissions from an aggregate perspective. Few studies have focused on nonlinear relationships and regional differences in China. Based on panel data of 1998–2014, this study uses the nonparametric additive regression model to explore the nonlinear effect of the high–tech industry from a regional perspective. The estimated results show that the residual sum of squares (SSR) of the nonparametric additive regression model in the eastern, central and western regions are 0.693, 0.054 and 0.085 respectively, which are much less those that of the traditional linear regression model (3.158, 4.227 and 7.196). This verifies that the nonparametric additive regression model has a better fitting effect. Specifically, the high–tech industry produces an inverted “U–shaped” nonlinear impact on CO2 emissions in the eastern region, but a positive “U–shaped” nonlinear effect in the central and western regions. Therefore, the nonlinear impact of the high–tech industry on CO2 emissions in the three regions should be given adequate attention in developing effective abatement policies.

Reducing CO2 emissions in China's manufacturing industry: Evidence from nonparametric additive regression models

Identifying the drivers of carbon dioxide emissions in the manufacturing industry is vital for developing effective environmental policies. This study adopts provincial panel data from 2000 to 2013 and uses nonparametric additive regression models to analyze the drivers of CO2 emissions in the industry. The results show that the nonlinear effect of economic growth on CO2 emissions supports the Environmental Kuznets Curve (EKC) hypothesis. Energy structure has an inverted “U-shape” effect owing to massive coal consumption in the early stages and the optimization of energy structure in the later stage. The inverted “U-shaped” impact of industrialization may be due to the priority development of heavy industry in the early stages and the optimization of industrial structure in the later stages. The impact of urbanization also exhibits an inverted “U-shaped” pattern because of mass consumption of steel and cement products in the early stages and the advancement in clean energy technologies at the later stages. However, specific energy consumption has a positive “U-shaped” impact because of the difference in the speed of technological progress at different times. Thus, the differential effects of these indicators at different times should be taken into consideration when discussing reduction of CO2 emissions in China's manufacturing industry.