Nonparametric Regression Method Research Articles

Elucidating pollution characteristics, temporal variation and source origins of carbonaceous species in Xinxiang, a heavily polluted city in North China

In order to understand temporal variations, sources origins of carbonaceous components in Xinxiang, an industry city in North China, high time resolution of OC and EC were observed from March 2021 to February 2022. The results illustrated annual average OC and EC concentrations were 5.76 ± 3.65 and 0.83 ± 0.56 μg m−3, respectively. Obvious seasonal and monthly fluctuations of carbonaceous components were observed with high values in cold seasons and low levels in warm seasons. Meanwhile, diurnal variation patterns of carbonaceous species illustrated temporal evolution of boundary layer height (BLH) and variation in emission intensity strongly affected carbonaceous component levels. In addition, obvious correlations between OC and EC (p < 0.001) were found with higher correlation coefficient in autumn, demonstrating they were be likely to originate from similar sources or POC contributed more to OC. The minimum R squared (MRS) method was adopted to calculate second organic carbon (SOC) concentration, represented 52%, 53%, 33%, and 52% of OC in spring, summer, autumn, and winter, respectively. Moreover, two different formation pathways (photochemical oxidation and heterogeneous reactions) of SOC were found in diverse seasons. Furthermore, nonparametric wind regression (NWR) method and potential source contribution function (PSCF) showed the sources from southeast, southwest, and northwest areas were considered as important contributors of carbonaceous species in Xinxiang. This work elucidates the significance of strict control precursors of carbonaceous components and the pressing requirements for coordinated inter−regional prevention and control of air pollution for further improving air quality.

Orthogonal series method for uncertain nonparametric regression with application to carbon dioxide emissions

Parametric regression is an important branch of statistics that assumes the regression model is known with a mathematical expression, while nonparametric regression has few restrictions on the regression model that is determined by the data. As a tool to explore the relationship between the observations characterized by uncertain variables, uncertain nonparametric regression has not obtained enough attention except for B-spline and local polynomial regression. In order to get a more global and smooth estimate, this paper employs the orthogonal series to approximate the nonparametric regression model. We intend to choose an appropriate number of the orthogonal bases by the leave-one-point-out cross-validation. Then, a new prediction technology is proposed to derive the response variable’s forecast value and confidence interval. Finally, a numerical example and a real data example of carbon dioxide emissions are put forward to demonstrate the effectiveness and accuracy of the method.

Investigation of Parametric, Non-Parametric and Semiparametric Methods in Regression Analysis

Regression analysis is known as statistical methods applied to model and analyze the relationship between variables. Regression method can be examined as parametric, non-parametric and semiparametric regression methods.&#x0D; The parametric regression method assumes that the dependent variable is in a linear relationship with the independent variables and that the shape of the relationship is known. If these assumptions are not met, non-parametric regression methods are applied. However, these methods cause difficulties especially in the interpretation part due to the problem of multidimensionality when there is more than one independent variable. Thus, when there is more than one independent variable, some of the independent variables may be in a linear relationship with the dependent variable, while the other part may be in a nonlinear relationship. Thus, in order to model these relationships, semiparametric regression methods, which are the additive combination of parametric and non-parametric regression methods, are used.&#x0D; In this study, parametric regression method, definition of non-parametric regression method and assumption conditions are given. It has been shown that the semiparametric regression method can be applied in cases where these assumptions are not met. Thus, in the study, regression methods were examined in three different parts, and parametric, non-parametric and semiparametric regression methods were examined theoretically.

PENDEKATAN REGRESI NONPARAMETRIK SPLINE UNTUK PEMODELAN INDEKS PEMBANGUNAN MANUSIA DI PULAU KALIMANTAN

The Human Development Index is a number that measures the achievement of human development based on a number of basic components of quality of life that can affect the level of productivity produced by a person. The calculation of the human development index can be based on three dimensions, namely the health dimension, the education dimension, the standard of living dimension In this study the method used is nonparametric spline regression. This nonparametric spline regression method is used to obtain the estimated regression curve through the data fitting approach. This method is also very suitable for use with data that changes frequently and does not determine a certain pattern. Spline is a model that has statistical and visual interpretation and has a very good ability to be generalized to complex and complex statistical models. The purpose of this study is to explain how the influence and how the best model of the number of health facilities, number of school facilities, economic growth, labor force participation rate and open unemployment rate on the human development index on the island of Kalimantan using nonparametric spline regression. The results of this study are the best model is at one knot point and the number of health facilities, the number of school facilities, economic growth, labor force participation rates and the open unemployment rate affect the dependent variable by 42.98 percent or can be said to be low, while the rest is explained by the variable others that are not included in the model.

PERMODELAN REGRESI NONPARAMETRIK SPLINE TERHADAP INFLASI DI PROVINSI KALIMANTAN SELATAN

Inflation is a condition of increasing prices continuously for a certain time. One of the factors thought to influence inflation, namely the Consumer Price Index (CPI), the Consumer Price Index (CPI) is an indicator that can be said to be important in determining the level of economic stability of a country. Seeing the relationship between the Consumer Price Index (CPI) and inflation, this study aims to explain how the influence and how the best model of the Consumer Price Index (CPI) on inflation in South Kalimantan Province uses Spline Nonparametric Regression. The use of the Spline Nonparametric Regression method in this study is because the data used has significant fluctuations so that it is estimated that the data is not normal. In the process, the Spline Nonparamteric Regression method is used to obtain the estimated regression curve through a data fitting approach. This method is also very suitable for use with data that changes frequently, spline is a model that has statistical, visual interpretation and has the ability to be generalized to complex and complex statistical models. The result of this research is that the best model is found at one knot point and the Consumer Price Index (CPI) has an effect on the inflation variable by 13.23 percent.Keywords: Inflation, Consumer Price Index, Spline Nonparametric Regression

A combined data-driven, experimental and modelling approach for assessing the optimal composition of impregnation products for cementitious materials

The effectiveness of sol-gel based treatments for the protection of concrete depends on their capacity to penetrate into the material pores. Optimization of sol formulation to achieve maximum penetration depth is not a straightforward process, as the influence of different physical properties of the sol varies with the pore size distribution of each concrete. Thus, a comprehensive experimental programme to evaluate this large number of materials would require a significant number of experiments. This manuscript describes an approach, using combined computational and experimental approach to design tailor-made impregnation products with optimized penetration depth on concrete or cementitious materials with different pore size distributions. First, a process-based numerical model, calibrated experimentally for one sol composition and several cementitious material samples with different pore structures is developed. The model calculates the penetration depth for a specific pore structure. The optimization process utilizes the probabilistic and non-parametric Gaussian Processes regression method Gaussian Processes at two steps; first to make the choice of the optimal experimental design, and second to make predictions of physical properties based on the obtained training points. In the final step, the penetration depth is calculated for each mix combination in defined parameter range. The effectiveness of this approach is demonstrated on three cases. In the first instance, we optimized the impregnation product for the maximum penetration depth without any restrictions. With another two cases, we impose the restrictions on the gelation time, i.e. the time in which the sol reacts to gel. The validation of the procedure has been made by the use of a blind validation and shows promising results. The impregnation product penetrated significantly deeper with a product selected by using the described procedure compared to the considered best product before this optimization. The proposed procedure can be applied to a wide range of cementitious materials based on their pore size distribution data. This offers significant advantage compared to purely experimental approaches, where a set of experiments is required for each considered material.

Spatial variation of the determinants affecting urban land value in Thiruvananthapuram, India

PurposeLand value varies at a micro level depending on the location’s economic, geographical and political determinants. The purpose of this study is to present a comprehensive assessment of the determinants affecting land value in the Indian city of Thiruvananthapuram in the state of Kerala.Design/methodology/approachThe global influence of the identified 20 explanatory variables on land value is measured using the traditional hedonic price modeling approach. The localized spatial variations of the influencing parameters are examined using the non-parametric regression method, geographically weighted regression. This study used advertised land value prices collected from Web sources and screened through field surveys.FindingsGlobal regression results indicate that access to transportation facilities, commercial establishments, crime sources, wetland classification and disaster history has the strongest influence on land value in the study area. Local regression results demonstrate that the factors influencing land value are not stationary in the study area. Most variables have a different influence in Kazhakootam and the residential areas than in the central business district region.Originality/valueThis study confirms findings from previous studies and provides additional evidence in the spatial dynamics of land value creation. It is to be noted that advanced modeling approaches used in the research have not received much attention in Indian property valuation studies. The outcomes of this study have important implications for the property value fixation of urban Kerala. The regional variation of land value within an urban agglomeration shows the need for a localized method for land value calculation.

Locally weighted regression for sunspots estimation and prediction

Locally weighted regression (LOESS) is a modern non-parametric regression method designed for treating cases where classical procedures are not highly efficient or cannot applied efficiently. Sunspots are the darker areas of the solar sphere's surface relative to other regions and are an important indicator of solar activity .The aim of this paper is to model and predict the number of sunspots because of their very importance to understanding the terrestrial consequences of solar activity and its direct impact on weather and communication systems on Earth, which may lead to damage to satellites. In this paper, the number of sunspots represented by annual data for the period from 1900 to 2021 (122 years) as well as monthly data for the period from January 1900 to January 2022 (1465 months) was obtained from the global data center (Sunspot Index and Long-term Solar Observations) (SILSO). The LOESS regression used for estimating and predicting the number of monthly and annual sunspots. The smoothing parameter, as well as the degree of the polynomial that fulfills the lowest for Akaike corrected information criterion. The analysis showed the ability of the LOESS to represent sunspot data by passing diagnostic tests as well as its high predictive ability. From the predictive values for the monthly data, it found that the maximum average number of sunspots will be 123.7 in July 2022, and the lowest average will be in February with 61.3 sunspots. Regarding the annual data, it found from the predictive values that the maximum average number of sunspots will be in the year 2023 with an average of 161.7 sunspots, and the lowest average will be in the year 2029 with an average of 16.1. Keywords: Locally weighted regression; sunspot; solar cycle; prediction.

Ranking Risk Factors in Financial Losses From Railroad Incidents: A Machine Learning Approach

The reported financial losses from railroad accidents since 2009 have been more than US$4.11 billion dollars. This considerable loss is a major concern for the industry, society, and the government. Therefore, identifying and ranking the factors that contribute to financial losses from railroad accidents would inform strategies to minimize them. To achieve that goal, this paper evaluates and compares the results of applying different non-parametric statistical and regression methods to 15 years of railroad Class I freight train accident data. The models compared are random forest, k-nearest neighbors, support vector machines, stochastic gradient boosting, extreme gradient boosting, and stepwise linear regression. The results indicate that these methods are all suitable for analyzing non-linear and heterogeneous railroad incident data. However, the extreme gradient boosting method provided the best performance. Therefore, the analysis used that model to identify and rank factors that contribute to financial losses, based on the gain percentage of the prediction accuracy. The number of derailed freight cars and the absence of territory signalization dominated as contributing factors in more than 57% and 20% of the accidents, respectively. Partial-dependence plots further explore the complex non-linear dependencies of each factor to better visualize and interpret the results.

Coverage error optimal confidence intervals for local polynomial regression

This paper studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for t statistics and coverage error expansions for interval estimators that (i) hold uniformly in the data generating process, (ii) allow for the uniform kernel, and (iii) cover estimation of derivatives of the regression function. The terms of the higher-order expansions, and their associated rates as a function of the sample size and bandwidth sequence, depend on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point is in the interior or on the boundary of the support. We prove that robust bias corrected confidence intervals have the fastest coverage error decay rates in all cases, and we use our results to deliver novel, inference-optimal bandwidth selectors. The main methodological results are implemented in companion R and Stata software packages.

Optimal development for a 3D-printed gripper for biomedical and micromanipulation applications by non-parametric regression-based metaheuristic technique

With the advancement of bioengineering and robotic engineering, medical robots have been increasing concern about manipulating the microobject or cells. Although the rigid robots have a stable operation, they inherit many limitations such as the complex assembly process of joints-coupled rigid links and expensive costs. Especially, clearances between kinematic joints cause vibrations that damage microobject. To cope with such problems, a flexure-based polylactic acid (PLA) gripper is developed to realize precise motion in medical robots. The proposed gripper is 3D printed by fused deposition modeling technique with advantages of monolithic structure, jointless and cheap cost. Prior to the gripper fabrication, the optimization development of the gripper is conducted employing a combination of the non-parametric regression (NPR) and multi-objective genetic algorithm (MOGA). Numerical data samples are collected by the finite element method. The modeling results were well formulated utilizing the NPR method with the R2 value greater than 0.9. The Pareto-optimum design results identified that the gripper can provide a high displacement of 2 mm and a small stress of 41 MPa via MOGA. Additionally, the proposed flexure-based compliant PLA gripper can work with a safety factor higher than 1.6. The experiment tests on the prototype of the gripper are close to the estimated values.

Nonparametric Quantile Regression for Homogeneity Pursuit in Panel Data Models

Many panel data have the latent subgroup effect on individuals, and it is important to correctly identify these groups since the efficiency of resulting estimators can be improved significantly by pooling the information of individuals within each group. However, the currently assumed parametric and semiparametric relationship between the response and predictors may be misspecified, which leads to a wrong grouping result, and the nonparametric approach hence can be considered to avoid such mistakes. Moreover, the response may depend on predictors in different ways at various quantile levels, and the corresponding grouping structure may also vary. To tackle these problems, this article proposes a nonparametric quantile regression method for homogeneity pursuit in panel data models with individual effects, and a pairwise fused penalty is used to automatically select the number of groups. The asymptotic properties are established, and an ADMM algorithm is also developed. The finite sample performance is evaluated by simulation experiments, and the usefulness of the proposed methodology is further illustrated by an empirical example.

Fractile Graphical Analysis in Finance: A New Perspective with Applications

Fractile Graphical Analysis (FGA) was proposed by Prasanta Chandra Mahalanobis in 1961 as a method for comparing two distributions at two different points (of time or space) controlling for the rank of a covariate through fractile groups. We use bootstrap techniques to formalize the heuristic method used by Mahalanobis for approximating the standard error of the dependent variable using fractile graphs from two independently selected “interpenetrating network of subsamples.” We highlight the potential and revisit this underutilized technique of FGA with a historical perspective. We explore a new non-parametric regression method called Fractile Regression where we condition on the ranks of the covariate and compare it with existing regression techniques. We apply this method to compare mutual fund inflow distributions after conditioning on ranks or fractiles of pre-tax and post-tax returns and compare distributions of private and public equity returns after controlling for fractiles of assets under management size using the two sample smooth test.

Multi-Output Regression with Generative Adversarial Networks (MOR-GANs)

Regression modelling has always been a key process in unlocking the relationships between independent and dependent variables that are held within data. In recent years, machine learning has uncovered new insights in many fields, providing predictions to previously unsolved problems. Generative Adversarial Networks (GANs) have been widely applied to image processing producing good results, however, these methods have not often been applied to non-image data. Seeing the powerful generative capabilities of the GANs, we explore their use, here, as a regression method. In particular, we explore the use of the Wasserstein GAN (WGAN) as a multi-output regression method. The resulting method we call Multi-Output Regression GANs (MOR-GANs) and its performance is compared to a Gaussian Process Regression method (GPR)—a commonly used non-parametric regression method that has been well tested on small datasets with noisy responses. The WGAN regression model performs well for all types of datasets and exhibits substantial improvements over the performance of the GPR for certain types of datasets, demonstrating the flexibility of the GAN as a model for regression.

Nonparametric kernel estimation of the probability of cure in a mixture cure model when the cure status is partially observed.

Cure models are a class of time-to-event models where a proportion of individuals will never experience the event of interest. The lifetimes of these so-called cured individuals are always censored. It is usually assumed that one never knows which censored observation is cured and which is uncured, so the cure status is unknown for censored times. In this paper, we develop a method to estimate the probability of cure in the mixture cure model when some censored individuals are known to be cured. A cure probability estimator that incorporates the cure status information is introduced. This estimator is shown to be strongly consistent and asymptotically normally distributed. Two alternative estimators are also presented. The first one considers a competing risks approach with two types of competing events, the event of interest and the cure. The second alternative estimator is based on the fact that the probability of cure can be written as the conditional mean of the cure status. Hence, nonparametric regression methods can be applied to estimate this conditional mean. However, the cure status remains unknown for some censored individuals. Consequently, the application of regression methods in this context requires handling missing data in the response variable (cure status). Simulations are performed to evaluate the finite sample performance of the estimators, and we apply them to the analysis of two datasets related to survival of breast cancer patients and length of hospital stay of COVID-19 patients requiring intensive care.

Investigation of affective traits affecting mathematics achievement by SEM and MARS methods

The purpose of the study is to analyze the affective traits that affect mathematics achievement through Structural Equation Modeling (SEM) as a traditional regression model and Multivariate Adaptive Regression Splines (MARS), as one of the data mining methods. Structural Equation Modeling, one of the regression-based methods, is quite popular for social sciences due to the various advantages it offers; however, it requires very intensive assumptions. MARS method, on the other hand, is a multivariate and adaptive nonparametric statistical regression method used for data classification and modeling. MARS does not need any assumptions such as normality, linearity, homogeneity. It allows variables that do not provide linearity to be included in the analysis. The present study examines whether it is possible to use the MARS method, which is a more flexible method compared to SEM, taking both methods into account. Regarding this goal, the SEM model was created with the program R using the affective data and the achievement variable picked from TIMMS 2019 data. Then, the MARS method was created using the SPM (Salford Predictive Modeler) program. The results of the study showed that at certain points the MARS model gave similar results to the SEM model and MARS model is more compatible with the literature.

Uniform convergence of local Fréchet regression with applications to locating extrema and time warping for metric space valued trajectories

Local Fréchet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general metric spaces from noisy metric space valued random objects. We derive uniform rates of convergence, which so far have eluded theoretical analysis of this method, for both fixed and random target trajectories, where we utilize tools from empirical processes. These results are shown to be widely applicable in metric space valued data analysis. In addition to simulations, we provide two pertinent examples where these results are important: The consistent estimation of the location of properly defined extrema in metric space valued trajectories, which we illustrate with the problem of locating the age of minimum brain connectivity as obtained from fMRI data; and time warping for metric space valued trajectories, illustrated with yearly age-at-death distributions for different countries.

Leadcare® II Comparison with Graphite Furnace Atomic Absorption Spectrophotometry for Blood Lead Measurement in Peruvian Highlands

Peru is one of the countries with the highest lead contamination in the world. Biological monitoring has limitations due to the shortage of laboratories with validated methodologies for the measurement of blood lead, and it is necessary to use alternative methods for its measurement in high-altitude cities. We aimed to compare the blood lead levels (BLL) measured by the LeadCare II (LC) method and Graphite Furnace Atomic Absorption Spectrometry (GF-AAS). We measured the BLL of 108 children from the city of La Oroya. The mean and median BLL for GF-AAS were 10.77 ± 4.18 and 10.44 µg/dL, respectively; for the LC method, the mean was 11.71 ± 4.28 and the median was 11.60 µg/dL. We found a positive linear correlation (Rho = 0.923) between both methods. Notwithstanding, the Wilcoxon test suggests a significant difference between both methods (ρ = 0.000). In addition, the Bland–Altman analysis indicates that there is a positive bias (0.94) in the LC method, and this method tends to overestimate the BLL. Likewise, we performed a generalized linear model to evaluate the influence of age and hemoglobin on BLL. We found that age and hemoglobin had a significant influence on BLL measured by the LC method. Finally, we used two non-parametric linear regression methods (Deming and Passing-Bablok regression) to compare the LC method with the GF-AAS. We found that these methods differ by at least a constant amount, and there would be a proportional difference between both. Although in general there is a positive linear correlation, the results of both methods differ significantly. Therefore, its use in cities located at high altitudes (higher than 2440 m.a.s.l.) would not be recommended.

Biomass Assessment and Carbon Sequestration in Post-Fire Shrublands by Means of Sentinel-2 and Gaussian Processes

In this contribution, we assessed the biomass and carbon stock of a post-fire area covered by a young oak coppice of Quercus pyrenaica Willd. associated with shrubs, mainly of Cistus laurifolius L. This area was burned during the fire event of Chequilla (Guadalajara, Spain) in 2012. Sentinel-2 imagery was used together with our own forest inventories in 2020 and machine learning methods to assess the total biomass of the area. The inventory includes plots of total dry weight ranging between 6 and 14 Mg·ha−1 with individuals up to 8 years old. Nonlinear, nonparametric Gaussian process regression methods were applied to link reflectance values from Sentinel-2 imagery with total shrub biomass. With a reduced inventory of only 32 plots covering 136 ha, the total biomass could be assessed with a root-mean-square error of 1.36 Mg·ha−1 and a bias of −0.04 Mg·ha−1, getting a relative error between 9.8% and 20.4% for the gathered biomass. This is a rather good estimation considering the little effort and time invested; thus, the suggested methodology is very suitable for forest monitoring and management.

Robust adaptive trajectory tracking for wheeled mobile robots based on Gaussian process regression

In this paper, we propose a novel learning-based robust adaptive trajectory tracking controller for wheeled mobile robots (WMR) subject to velocity input uncertainties. Gaussian process regression (GPR) is employed in view of its powerful estimation ability and wide scope of applications as a nonparametric regression method. The velocity uncertainties are estimated online using the real-time measured data. The prediction mean and variance of the GPR are used to counteract the effect of the uncertainties and to design the robust control term, respectively. A continuous robust controller is proposed which has the advantage of achieving asymptotic convergence of the trajectory tracking error instead of uniformly ultimately boundedness. Comparisons with the neural network based adaptive controller and a state of the art GPR-based design demonstrate the effectiveness of the proposed control strategy.