Nonparametric Kernel Regression Research Articles

Modeling of Economic Growth Rate in West Nusa Tenggara Province with Longitudinal Kernel Nonparametric Regression

Economic growth can indicate the success of economic development in people's lives, so it is essential to study the relationship between economic growth and factors that affect economic growth. Regression analysis is one of the most widely used statistical data analysis methods to determine the relationship pattern between the independent and dependent variables. Three methods can be used to estimate the regression curve, one of which is nonparametric regression. Economic growth data is one form of longitudinal data, with observations of independent subjects, with each subject being observed repeatedly over different periods. Kernel nonparametric regression model applications can be used for longitudinal data. This research aims to estimate the curve and get the best regression model. In this research, the smoothing technique chosen to estimate the nonparametric regression model for longitudinal data is the kernel triangle estimator, which can be obtained by minimizing the square of error using Weighted Least Squares (WLS) and selecting the optimum bandwidth using the Generalized Cross Validation (GCV) method. This study uses the economic growth rate in West Nusa Tenggara as the dependent variable and the human development index, population density, general allocation funds, local revenue, and labor force participation as independent variables. The result showed that the model is less accurate because of the low value of the coefficient for determination and the high value of the mean absolute percentage error (MAPE). This can be caused by the selection of bandwidth intervals that are too small.

FINKER: Frequency Identification through Nonparametric KErnel Regression in astronomical time series

Optimal frequency identification in astronomical datasets is crucial for variable star studies, exoplanet detection, and asteroseismology. Traditional period-finding methods often rely on specific parametric assumptions, employ binning procedures, or overlook the regression nature of the problem, limiting their applicability and precision. We introduce a universal, nonparametric kernel regression method for optimal frequency determination that is generalizable, efficient, and robust across various astronomical data types. FINKER uses nonparametric kernel regression on folded datasets at different frequencies, selecting the optimal frequency by minimising squared residuals. This technique inherently incorporates a weighting system that accounts for measurement uncertainties and facilitates multi-band data analysis. We evaluated our method's performance across a range of frequencies pertinent to diverse data types and compared it with an established period-finding algorithm, conditional entropy. The method demonstrates superior performance in accuracy and robustness compared to existing algorithms, requiring fewer observations to reliably identify significant frequencies. It exhibits resilience against noise and adapts well to datasets with varying complexity.

Application of the evolutionary approach to structural and parametric identification of dynamic objects

The paper examines the evolutionary approach to structural and parametric identification of dynamic systems in the form of differential equations. The approach is based on a genetic programming algorithm to determine a structure of the equation and differential evolution method for parameters selection. The author proposed approach based on such evolutionary algorithms as genetic programming and differential evolution. The search for the structure is carried out by genetic programming. The selection of numerical parameters and initial conditions is implemented by a method of differential evolution. The problem of finding a model that describes changes in the efficiency of a hydraulic system is solved with the help of this approach. The proposed approach is compared with a recurrent neural network and a nonparametric kernel regression estimation.

Exploring the Role of Institutional Governance in Climate Action in the Western Balkans Economies

The new United Nations (UN) sustainable development (SD) agenda in 2015 heralded the beginning of a new global effort for the planet's sustainability through the Sustainable Development Goals (SDGs). They provide a framework for all countries, regardless of income levels, to guide national planning for achieving SD. Climate change may impact almost all SDGs and vice versa, though, of the 17 SDGs, the 13th is designated to climate action. The growing concern for environmental degradation has raised the question of how countries will manage to achieve SDGs and whether the answer can be found in their institutions. Reducing emissions necessitates environmental policies influenced by political institutions that shape policy adoption and implementation. This paper aims to analyze the effects of institutions adopting the dimensions of good governance on particular SDG indicators of the 13th SDG by using a Nonparametric Kernel Regression framework and a panel data set of 5 Western Balkans (WB) countries from 2000 to 2020. The target countries share the ambition of EU accession and hold the EU candidate status. WB countries spark our interest because of the severe institutional governance problems, which limit their ability to progress towards SDGs. The paper's empirical analysis uses a specific SDG indicator for the 13 SDG of the Europe Sustainable Development Report, similar to that used by the OECD for the report on Measuring Distance to the SDG Targets. The analysis includes as independent variables the World Governance Indicators (WGI). Contributing to the existing literature on institutions and SD, the novelty of our approach is the use of the WGI with SDG indicators in measuring the impact of quality of governance on the progress towards the 13th SDG referring to climate action.

Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression

The presence of nonignorable missing response variables often leads to complex conditional distribution patterns that cannot be effectively captured through mean regression. In contrast, quantile regression offers valuable insights into the conditional distribution. Consequently, this article places emphasis on the quantile regression approach to address nonrandom missing data. Taking inspiration from fractional imputation, this paper proposes a novel smoothed quantile regression estimation equation based on a sampling importance resampling (SIR) algorithm instead of nonparametric kernel regression methods. Additionally, we present an augmented inverse probability weighting (AIPW) smoothed quantile regression estimation equation to reduce the influence of potential misspecification in a working model. The consistency and asymptotic normality of the empirical likelihood estimators corresponding to the above estimating equations are proven under the assumption of a correctly specified parameter working model. Furthermore, we demonstrate that the AIPW estimation equation converges to an IPW estimation equation when a parameter working model is misspecified, thus illustrating the robustness of the AIPW estimation approach. Through numerical simulations, we examine the finite sample properties of the proposed method when the working models are both correctly specified and misspecified. Furthermore, we apply the proposed method to analyze HIV—CD4 data, thereby exploring variations in treatment effects and the influence of other covariates across different quantiles.

The Finite Sample Performance of Instrumental Variable-Based Estimators of the Local Average Treatment Effect When Controlling for Covariates

AbstractThis paper investigates the finite sample performance of a range of parametric, semi-parametric, and non-parametric instrumental variable estimators when controlling for a fixed set of covariates to evaluate the local average treatment effect. Our simulation designs are based on empirical labor market data from the US and vary in several dimensions, including effect heterogeneity, instrument selectivity, instrument strength, outcome distribution, and sample size. Among the estimators and simulations considered, non-parametric estimation based on the random forest (a machine learner controlling for covariates in a data-driven way) performs competitive in terms of the average coverage rates of the (bootstrap-based) 95% confidence intervals, while also being relatively precise. Non-parametric kernel regression as well as certain versions of semi-parametric radius matching on the propensity score, pair matching on the covariates, and inverse probability weighting also have a decent coverage, but are less precise than the random forest-based method. In terms of the average root mean squared error of LATE estimation, kernel regression performs best, closely followed by the random forest method, which has the lowest average absolute bias.

Bandwidth selection for treatment choice with binary outcomes

This study considers the treatment choice problem when the outcome variable is binary. We focus on statistical treatment rules that plug in fitted values from a nonparametric kernel regression, and show that the maximum regret can be calculated by maximizing over two parameters. Using this result, we propose a novel bandwidth selection method based on the minimax regret criterion. Finally, we perform a numerical exercise to compare the optimal bandwidth choices for binary and normally distributed outcomes.

A-050 Understanding the Complex Relationship Between TSH and Free Thyroxine

Abstract Background Guidelines suggest screening for thyroid disease using thyroid stimulating hormone (TSH) first before free thyroxine (fT4) since there is an inverse log-linear relationship between them; the signal favors TSH over fT4 in a ratio of >100:2. We reassessed this fT4 to TSH relationship following the improved 3rd generation TSH assay from Roche (since 09/2019). Methods Consecutive paired TSH/fT4 (n = 7484) from distinct ambulatory non-hospitalized subjects that were assayed on cobas e801 were retrieved from our laboratory information system and combined with similar data from Kuala Lumpur Hospital (n = 11 369) that were assayed on cobas e601. Reference intervals and measuring limits for the Roche assays were 0.4–4.0 μIU/L and 0.005–100 μIU/L for TSH, and fT4 10–20 pmol/L and 0.3–100 pmol/L for fT4, respectively. Values outside the reportable limits (n = 618) were excluded. Descriptive statistics, linear and nonparametric (kernel) regression were performed using the statistical software packages in R 4.2.0. Results Linear regression of logTSH against fT4 (n = 18 235) gave an r = −0.35. Nonparametric regression revealed two negative sigmoid curves merging into the euthyroxinemic region (see Graph). Three different segments can be discerned; hypothyroxinemic (fT4 < 10): logTSH = 1.91–0.136fT4 (n = 422; r = −0.39, P < 0.001), euthyroxinemic (fT4 10–20): logTSH = 0.672–0.028fT4 (n = 15 754, r = −0.13, P < 0.001), and hyperthyroxinemic (fT4>20): logTSH = 1.106–0.055fT4 (n = 2059, r = −0.33, P < 0.001). Conclusion The relationship between fT4 and TSH is complex. The widely accepted view of a constant gradient of logTSH against fT4 over the whole range of thyroid test values is inaccurate. Three distinct relationships correspond to each biochemical thyroid status. In the hypothyroxinemic and hyperthyroxinemic range, TSH increases almost 5-fold and 13-fold with a doubling of fT4, respectively. In the euthyroxinemic range, there is no relationship between logTSH and fT4. While a TSH first strategy is applicable in hypo/hyperthyroxinemia, both TSH/fT4 are still required to confirm diagnoses and for baseline assessment prior to commencing therapy.

The impact of natural resource management, innovation, and tourism development on environmental sustainability in low-income countries

Natural resource depletion and the effects of global warming on the environment have emerged as urgent worldwide challenges. Many countries have responded by implementing plans to manage their natural resources and deal with environmental issues in the post-COVID-19 era. However, innovative abilities are frequently limited in low-income countries (LICs), which makes it difficult for them to successfully offset environmental consequences. It is crucial to comprehend the possible contributions that innovation, tourism, and the availability of natural resources can make to resolving these issues. This study focuses on examining how innovation, tourism, and environmental degradation relate to LICs richness of natural resources. To establish the reliability of the results, empirical analysis utilizing data from 2000 to 2020 of LICs was carried out using the Feasible GLS, Prais-Winsten Regression, Driscoll-Kraay standard error regression, and Non-Parametric Kernel regression models. The findings show that natural resources have a beneficial effect on environmental degradation in LICs. Natural resource-dependent sectors are thought to use energy-intensive procedures, which contribute to greater emissions, in countries where the share of natural resource rent in GDP is higher. Higher levels of innovation may not always result in environmental sustainability in LICs, as the study also demonstrates a positive association between innovation and environmental degradation. Although there is a link between tourism and environmental deterioration, it is possible that the growth of tourism in LICs will encourage the transition to a less carbon-intensive service-based economy.

Supervised kernel principal component analysis for forecasting

Principal component analysis (PCA) is a versatile tool for dimension reduction with many applications in finance, economics, and machine learning. This paper proposes a new approach to improving the forecasting ability of the Principal Components (PCs) of observed high-dimensional predictors in a factor-augmented forecasting framework. The approach is carried out in a three-step procedure, where we first perform a nonparametric kernel regression of the target variable on each predictor to obtain a new high-dimensional predictor vector formed by stacking all estimated kernel regression functions, we then extract PCs from these new predictors using PCA, and finally, we employ the extracted PCs as predictors to forecast the target variable. A real example on macroeconomic forecasting is analyzed and numerical results show that the proposed kernel PCA can outperform some commonly used forecasting approaches in out-of-sample prediction.

PERAMALAN INDEKS JAKARTA ISLAMIC INDEX (JII) DENGAN PENDEKATAN REGRESI PARAMETRIK LINIER SEDERHANA DAN REGRESI NONPARAMETRIK KERNEL DILENGKAPI GUI R-SHINY

Investment in Islamic stocks in Indonesia has increased from 2019 to 2021. One of the references for investors in monitoring Islamic stock price movements is the Jakarta Islamic Index_(JII). The_purpose_of_this_research_is_to model the index (JII) using nonparametric kernel regression. The kernel_functions_used_in nonparametric regression are Gaussian, Uniform, Triangle, and Epanechnikov._The research data-is-divided-into-In-Sample-data-for the period January-2010-to-December 2020 and-Out-Sample-data.for the_period_January_2021_to_December_2021. The_best_model_is selected based_on_the smallest MSE-value-obtained by the Triangle kernel regression with an optimum bandwidth (h) of 48, 2. The R2 value is 0.897. Based on the criteria for the R2 value, it-can-be-stated that_the_best model_is_a strong model_with a proportion of_the influence-of-the-previous index-on-the.current index value of-89.7%, and-there-maining_10.3%_is_influenced_by_other_factors.-The best model forecasting ability can be seen from the MAPE data out sample value of 3.04%, which is less than 10%, meaning that the performance of the kernel model in predicting the JII index is very good. This research uses R software which is equipped with R-Shiny GUI to help with data processing.

Kernel Nonparametric Regression for Forecasting Local Original Income

Regional Original Revenue (ROR) is an income collected based on regional regulations under statutory regulations. ROR aims to give authority to Regional Governments to sponsor the implementation of regional autonomy following regional potential. Every year, the Central Lombok Regency government sets ROR targets to assist the government in formulating regional policies. The targets set by the government are sometimes not following their realization. This study aims to determine a model that can be used in forecasting ROR targets. One way to predict the value of ROR is by using a nonparametric regression approach. This approach is flexible since it is not dependent on a particular model. The use of the nonparametric kernel regression method with the Gaussian kernel function obtained a minimum GCV value of 1,769688931 with an optimum bandwidth value of of 0,212740452 and of 0,529682589. Modeling with optimum bandwidth produces a coefficient of determination of 87,55%. The best model is used for forecasting and produces a MAPE value of 5,4%. The analysis results show that what influences the value of ROR is ROR receipts in the previous month and the previous 12 months.

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.

Anatomical and functional remodeling of left ventricle in patients with primary aldosteronism and concomitant albuminuria.

Primary aldosteronism (PA) is the leading cause of secondary hypertension globally and is associated with adverse cardiovascular outcomes. However, the cardiac impact of concomitant albuminuria remains unknown. To compare anatomical and functional remodeling of left ventricle (LV) in PA patients with or without albuminuria. Prospective cohort study. The cohort was separated into two arms according to the presence or absence of albuminuria (>30 mg/g of morning spot urine). Propensity score matching with age, sex, systolic blood pressure, and diabetes mellitus was performed. Multivariate analysis was conducted with adjustments for age, sex, body mass index, systolic blood pressure, duration of hypertension, smoking, diabetes mellitus, number of antihypertensive agents, and aldosterone level. A local-linear model with bandwidth of 2.07 was used to study correlations. A total of 519 individuals with PA were enrolled in the study, of whom 152 had albuminuria. After matching, the albuminuria group had a higher creatinine level, at baseline. With regard to LV remodeling, albuminuria was independently associated with a significantly higher interventricular septum (1.22 > 1.17 cm, p = 0.030), LV posterior wall thickness (1.16 > 1.10 cm, p = 0.011), LV mass index (125 > 116 g/m2, p = 0.023), and medial E/e' ratio (13.61 > 12.30, p = 0.032), and a lower medial early diastolic peak velocity (5.70 < 6.36 cm/s, p = 0.016). Multivariate analysis further revealed that albuminuria was an independent risk factor for elevated LV mass index (p < 0.001) and medial E/e' ratio (p = 0.010). Non-parametric kernel regression also demonstrated that the level of albuminuria was positively correlated with LV mass index. The remodeling of LV mass and diastolic function under the presence of albuminuria distinctly improved after PA treatment. The presence of concomitant albuminuria in patients with PA was associated with pronounced LV hypertrophy and compromised LV diastolic function. These alterations were reversible after treatment for PA. Cardiac Impact of Primary Aldosteronism and Albuminuria Primary aldosteronism and albuminuria has been, respectively, demonstrated to bring about left ventricular remodeling, but the aggregative effect was unknown. We constructed a prospective single-center cohort study in Taiwan. We proposed the presence of concomitant albuminuria was associated with left ventricular hypertrophy and compromised diastolic function. Intriguingly, management of primary aldosteronism was able to restore these alterations. Our study delineated the cardiorenal crosstalk in the setting of secondary hypertension and the role of albuminuria for left ventricular remodeling. Future interrogations toward the underlying pathophysiology as well as therapeutics will facilitate the improvement of holistic care for such population.

Weak consistency for the nonparametric kernel regression estimator based on negatively associated random errors

In this article, we mainly study the weak consistency for the Gasser and Müller (G-M) kernel estimator (a weighted kernel estimator with integral form) in a nonparametric regression model based on negatively associated random errors under some suitable conditions. In addition, a simulation to study the numerical performance of the consistency for the G-M estimator is provided.

Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models

The self-similar gravitational collapse solutions to the Einstein-axion–dilaton system have already been discovered. Those solutions become invariants after combining the spacetime dilation with the transformations of internal SL(2, R). We apply nonlinear statistical models to estimate the functions that appear in the physics of Black Holes of the axion–dilaton system in four dimensions. These statistical models include parametric polynomial regression, nonparametric kernel regression and semi-parametric local polynomial regression models. Through various numerical studies, we reached accurate numerical and closed-form continuously differentiable estimates for the functions appearing in the metric and equations of motion.

Patient-Reported Rectal QOL with Pelvic Nodal Irradiation ± Involved Pelvic Nodal Boost to 75 Gy EQD2 in Men with Prostate Cancer

<h3>Purpose/Objective(s)</h3> The study was designed to compare patient-reported acute and late rectal function quality of life (RQOL) between men with local or regional prostate cancer treated with or without an involved pelvic nodal simultaneous integrated boost (SIB). It is hypothesized that men receiving pelvic nodal radiotherapy at 50.4 Gy in 28 fractions (Pelv50) have similar RQOL as men receiving the same pelvis dose plus the addition of involved pelvic nodal SIB to 67.2 Gy in 28 fractions (Pelv67). <h3>Materials/Methods</h3> Rectal toxicity was assessed using the Merrick Rectal Function Assessment Score (R-FAS). The R-FAS consists of nine questions and a scoring range of 0-27, with higher scores indicating poorer bowel function. Patients with measures -180 days and up to 730 days from the start of RT were included in the analysis. SIB targets included radiographically apparent nodal GTVs plus a 5mm margin. Pelvic nodal contours extended from aortic bifurcation through the bilateral obturator nodes. An EQD2 of 75 Gy to involved nodal targets was calculated for the Pelv67 group based on 28 fractions of 2.4 Gy with an α/β ratio of 1.5. Patients were dichotomized by treatment received (Pelv50 vs. Pelv67). Non-parametric kernel regression was modeled with R-FAS score as the dependent variable and time from RT and treatment cohort as the independent variables, with improved Akaike information criterion to determine optimal bandwidth. Marginal means and 95% confidence intervals were predicted at 90-day intervals from timepoint 0 with 50 bootstrapping replications. <h3>Results</h3> There was no difference in baseline age or baseline Charlson Comorbidity Index between the two cohorts. There was no significant difference in mean R-FAS over the entire time interval between the two cohorts (Pelv67 vs. Pelv50: 0.4 points, p=0.17). There is no significant difference in R-FAS score at any discrete timepoint between Pelv67 and Pelv50 as the 95% confidence intervals overlap (Table). <h3>Conclusion</h3> Pelvic nodal irradiation with a simultaneous integrated boost to 67.2 Gy in 28 fractions (EQD2=75 Gy) was associated with similar rates of RQOL compared to standard pelvic irradiation from the patient's perspective. This study suggests that dose escalation using a pelvic nodal SIB technique to 75Gy EQD2 is safe despite the proximity of the rectum and bowel to SIB targets.

Non-parametric Multivariate Kernel Regression Estimation to Describe Cognitive Processes and Mental Representations

In this research paper, we set forward a non-parametric multivariate recursive kernel regression estimator under missing data using the propensity score approach in order to describe writing word production. Our main objective is to explore cognitive processes and mental representations mobilized when a human being prepares to write a word according to the idea developed in Perret and Olive (2019). We investigate the asymptotic properties of the proposed recursive estimator and compare them to the well known Nadaraya-Watson’s regression estimator. We calculate the bias and the variance of the proposed estimator which depend on the choice of some parameters such as the stepsize and the bandwidth. We examine some data-driven procedures to select these parameters. Thus, we demonstrate that, under some optimal choices of these parameters, the MSE (Mean Squared Error) of the proposed estimator can be smaller than the one obtained by using Nadaraya Watson’s regression estimator. The elaborated estimator is then applied to the behavioral data to classify some participants in groups. This classification may stand for a departure point to tackle written behavior variations.

Asymptotic Normality of the Robust Equivariant Estimator for Functional Nonparametric Models

As in parametric regression, nonparametric kernel regression is essential for examining the relationship between response variables and covariates. In both methods, outliers may affect the estimators, and hence robustness is essential to deal with practical issues. This paper proposes a family of robust nonparametric estimators with unknown scale parameters for regression function based on the kernel method. In addition, we establish the asymptotic normality of the estimator under the concentration properties on small balls of probability measure of the functional explanatory variables. The superiority of the proposed methods is shown through numerical and real data studies to compare the sensitivity to outliers between the classical and robust regression (fixed and unknown scale parameter). Such a new proposed method will be useful in the future for analyzing data and making decisions.

Fast aerial image model for EUV lithography using the adjoint fully convolutional network

The effects of thick-mask and oblique incidence in extreme ultraviolet (EUV) lithography system make the aerial image calculation a challenging task. This paper develops a fast EUV lithography aerial image model based on a new kind of deep learning framework called adjoint fully convolutional network (AFCN). The AFCN consists of two adjoint data paths to respectively recover the real part and imaginary part of the complex mask diffraction-near-field (DNF). The feature-swapping technique is introduced to exchange the information between the real and imaginary data paths. The AFCN is trained based on a pre-calculated rigorous thick-mask DNF dataset. Given the estimated thick-mask DNF, the Abbe's method is used to calculate the aerial image of the partially coherent lithography system. Compared to the traditional non-parametric kernel regression method, the proposed model reduces the error by more than 80% and achieves 25-fold improvement in computational efficiency.