Optimal Bandwidth Selection Research Articles

A semiparametric Gaussian mixture model for chest CT-based 3D blood vessel reconstruction.

Computed tomography (CT) has been a powerful diagnostic tool since its emergence in the 1970s. Using CT data, 3D structures of human internal organs and tissues, such as blood vessels, can be reconstructed using professional software. This 3D reconstruction is crucial for surgical operations and can serve as a vivid medical teaching example. However, traditional 3D reconstruction heavily relies on manual operations, which are time-consuming, subjective, and require substantial experience. To address this problem, we develop a novel semiparametric Gaussian mixture model tailored for the 3D reconstruction of blood vessels. This model extends the classical Gaussian mixture model by enabling nonparametric variations in the component-wise parameters of interest according to voxel positions. We develop a kernel-based expectation-maximization algorithm for estimating the model parameters, accompanied by a supporting asymptotic theory. Furthermore, we propose a novel regression method for optimal bandwidth selection. Compared to the conventional cross-validation-based (CV) method, the regression method outperforms the CV method in terms of computational and statistical efficiency. In application, this methodology facilitates the fully automated reconstruction of 3D blood vessel structures with remarkable accuracy.

The performance of mixed truncated spline-local linear nonparametric regression model for longitudinal data

A mixed estimator nonparametric regression (MENR) model is an additive model that involves a combination of two estimators or more in multivariable nonparametric regression. The model is used when there are differences in data patterns among predictor variables. This study proposes the development of the MENR model on longitudinal data namely a mixed truncated spline-local linear nonparametric regression (MTSLLNR) model. A modified weighted least square (WLS) method through two-stage estimation is used to estimate the regression function in the proposed model. To illustrate the performance of the MTSLLNR model, a simulation study with a sample size variation of subjects and time points is provided. Additionally, the MTSLLNR model is also applied to model the poverty gap index data. Both simulated and real data results suggest that the proposed model has consistency findings and good performance in longitudinal data modeling. Some highlights of the proposed method are:•The method combines two estimators of local linear and truncated spline to accommodate the differences in data patterns in the nonparametric regression for longitudinal data.•Selection of optimal knots and bandwidth using the generalized cross-validation (GCV) method.•The consistency findings and general performance of the method is shown by simulation and real data application.

Analisis Data Time Series Menggunakan Model Kernel: Pemodelan Data Harga Saham MDKA

<p>Classic time series data analysis techniques, such as autoregressive, model stationary data in which the values of prior observations influence the current observations through a process known as linear regression. There are several requirements for error assumptions in autoregressive, including independence, normal distribution with a zero mean and constant variance. It is frequently discovered that these assumptions are challenging to verify when modelling real data. Kernel time series regression is an alternative model that does not require error assumptions. Non-stationary time series data can be effectively modelled using the kernel time series method. Time series data that isn't yet stationary is made stationary first, then the data is modified by forming the current stationary time series data as the response variable and the previous period data as the predictor variable. Next, regression kernel modelling is carried out while applying kernel weight function and determining the optimal bandwidth. For development of science, the optimal bandwidth can be achieved by minimizing the MSE, CV, GCV, or UBR values. It is possible to use R<sup>2</sup> or MAPE as the kernel time series regression model's goodness metric. A strong model is generated while modelling MDKA stock price data using kernel regression utilizing the Gaussian kernel function and optimal bandwidth selection using GCV since R<sup>2</sup> is 0.9828372 more than 0.67 and MAPE is 1.985681% under 10%.</p><p><strong>Keywords</strong><strong>: </strong>3 time series; kernel regression; GCV; MDKA stock price.</p>

A GPU-Accelerated Method for 3D Nonlinear Kelvin Ship Wake Patterns Simulation

The study of ship waves is important for ship detection, coastal erosion and wave drag. This paper proposed a highly paralleled numerical computation method for efficiently simulating three-dimensional nonlinear kelvin waves. First, a numerical model for nonlinear ship waves is established based on potential flow theory, the Jacobian-free Newton–Krylov (JFNK) method and the boundary integral method. To reduce the amount of data stored in the JFNK method and improve the computational efficiency, a banded preconditioner method is then developed by formulating the optimal bandwidth selection rule. After that, a Graphics Process Unit (GPU)-based parallel computing framework is designed, and we used the Compute Unified Device Architecture (CUDA) language to develop a GPU solution. Finally, numerical simulations of 3D nonlinear ship waves under multiple scales are performed by using the GPU and CPU solvers. Simulation results show that the proposed GPU solver is more efficient than the CPU solver with the same accuracy. More than 66% GPU memory can be saved, and the computational speed can be accelerated up to 20 times. Hence, the computation time for Kelvin ship waves simulation can be significantly reduced by applying the GPU parallel numerical scheme, which lays a solid foundation for practical ocean engineering.

Optimal Bandwidth Selection Methods with Application to Wind Speed Distribution

Accurate estimation of the unknown probability density functions of critical variables, such as wind speed—which plays a pivotal role in harnessing clean energy—is essential for various scientific and practical applications. This research conducts a comprehensive comparative analysis of seven distinct bandwidth calculation techniques across various normal distributions, using simulation as the evaluation method in the context of Kernel Density Estimation (KDE). This analysis includes the calculation of the optimal bandwidth and assessment of the performance of these methods with respect to Mean Squared Error (MSE), bias, and the optimal bandwidth value. The findings reveal that among the various bandwidth methods evaluated, the Bandwidth bandwidth-based Cross-Validation (BCV), especially for small sample sizes, consistently provides the closest result to the optimal bandwidth across most of the applied normal distributions. These results provide valuable insights into the selection of optimal bandwidths for accurate and reliable density estimation in the context of normal distributions. Another key aspect of this work is the extension of these methods to wind speed data in a specific region. Monthly wind speed kernel density estimates obtained using all seven bandwidth selection techniques show that Smoothed Cross-Validation (SCV) is suited for this type of real-world data.

A novel adaptive multi-scale Rényi transfer entropy based on kernel density estimation

The utilization of Rényi Transfer Entropy (RTE) as a powerful model for analyzing causal relationships among variables has become pervasive in the field of complex systems time series causality detection. However, there are two major challenges in using RTE: the inherent multilevel structure of causal associations in the systems, and the precision in RTE estimation. To address these challenges, this paper proposes an adaptive multi-scale Rényi transfer entropy based on kernel density estimation. The framework of causal detection based on the novel RTE consists of two parts: adaptive discrete wavelet transform (ADWT)-based time series decomposition and multivariate kernel density estimation (MKDE)-based causality network generation. In the ADWT-based time series decomposition, the original series are decomposed into different frequency bands by optimal wavelet coefficients, which is generated adaptively by an auto-encoder. In the MKDE-based causality network generation, the causal network between the variables is represented by an adjacency matrix composed of their decomposition components in each layer, and the values of the matrix are the RTE values between the variables. In order to accurate estimation of RTE values an evaluation criterion for KDE under a uniform measure in both univariate and multivariate cases and the optimal bandwidth selection is provided in this part. To validate the effectiveness of the novel causal measure in this paper, the proposed method is tested on the synthetic and real data, and the results show that it can effectively detect causal relationships among variables at different levels in non-stationary time series of both bidirectional and undirectional complex systems. Compared to the other RTE estimators, the proposed method can detect the causality accurately and avoid the spurious causality.

Day-ahead interval scheduling strategy of power systems based on improved adaptive diffusion kernel density estimation

The increasing penetration of renewable energy causes high uncertainty, which further complicates the optimal scheduling operation of power systems. The uncertainty of renewable energy output is represented by empirical prediction intervals in the traditional interval optimization scheduling model, but the interval range is not precise enough. To address this problem, a novel improved interval optimization method is proposed in this paper. First, the improved adaptive diffusion kernel density estimation (IADKDE) is used to obtain more accurate intervals for the renewable energy output. Furthermore, a data-driven adaptive optimal bandwidth selection is adopted to select the optimal bandwidth instead of normal reference rules in IADKDE. In addition, the day-ahead scheduling optimization model is developed by IADKDE considering the driving requirements of electric vehicles (EVs) owners. The proposed model is described in details and solved by interval linear programming method. Finally, the effectiveness and accuracy of the proposed method are validated, and the comparative analysis with interval optimization by empirical prediction intervals, extreme learning machine(ELM) and stochastic optimization is given. It is demonstrated that the proposed method can obtain more accurate interval ranges of uncertain variables and has strong applicability.

LIMIT THEORY FOR LOCALLY FLAT FUNCTIONAL COEFFICIENT REGRESSION

Functional coefficient (FC) regressions allow for systematic flexibility in the responsiveness of a dependent variable to movements in the regressors, making them attractive in applications where marginal effects may depend on covariates. Such models are commonly estimated by local kernel regression methods. This paper explores situations where responsiveness to covariates is locally flat or fixed. The paper develops new asymptotics that take account of shape characteristics of the function in the locality of the point of estimation. Both stationary and integrated regressor cases are examined. The limit theory of FC kernel regression is shown to depend intimately on functional shape in ways that affect rates of convergence, optimal bandwidth selection, estimation, and inference. In FC cointegrating regression, flat behavior materially changes the limit distribution by introducing the shape characteristics of the function into the limiting distribution through variance as well as centering. In the boundary case where the number of zero derivatives tends to infinity, near parametric rates of convergence apply in stationary and nonstationary cases. Implications for inference are discussed and a feasible pre-test inference procedure is proposed that takes unknown potential flatness into consideration and provides a practical approach to inference.

Optimal bandwidth selection for retrieving Cu content in rock based on hyperspectral remote sensing

Optimal bandwidth selection for retrieving Cu content in rock based on hyperspectral remote sensing

Lpdensity: Local Polynomial Density Estimation and Inference

Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their well-known boundary bias. Alternative smoothing methods are available to handle boundary points in density estimation, but they all require additional tuning parameter choices or other typically ad hoc modifications depending on the evaluation point and/or approach considered. This article discusses the R and Stata package lpdensity implementing a novel local polynomial density estimator proposed and studied in Cattaneo, Jansson, and Ma (2020, 2022), which is boundary adaptive and involves only one tuning parameter. The methods implemented also cover local polynomial estimation of the cumulative distribution function and density derivatives. In addition to point estimation and graphical procedures, the package offers consistent variance estimators, mean squared error optimal bandwidth selection, robust bias-corrected inference, and confidence bands construction, among other features. A comparison with other density estimation packages available in R using a Monte Carlo experiment is provided.

Cosine-based variable bandwidth selection for nonparametric spectral density estimation under long-range dependence

The optimal bandwidth selection in kernel-based nonparametric density estimation is one of the important parts in the spectral density estimation under long-range dependence (LRD). To improve the performance of the nonparametric spectral density estimation (NPSDE) under LRD, we propose a new cosine-based variable bandwidth selection method, which is motivated by variable bandwidth selection for density estimation and spectral density for autoregressive fractionally-integrated moving average models. The performance of the proposed method was illustrated through the simulation studies and data examples. The proposed cosine-based variable bandwidth selection method for NPSDE under LRD provides better performance than any other bandwidth selection method. Our method is robust to any values of the fractional differencing parameters.

Mixed estimator of spline truncated, Fourier series, and kernel in biresponse semiparametric regression model

Regression analysis is a method of analysis to determine the relationship between the response and the predictor variables. There are three approaches in regression analysis, namely the parametric, nonparametric, and semiparametric approaches. Biresponse Semiparametric regression model is a regression model that uses a combination approach between parametric and nonparametric components, where two response variables are correlated with each other. For data cases with several predictor variables, different estimation technique approaches can be used for each variable. In this study, the parametric component is assumed to be linear. At the same time, the nonparametric part is approached using a mixture of three estimation techniques, namely, spline truncated, Fourier series, and the kernel. The unknown data pattern is assumed to follow the criteria of each of these estimation techniques. The spline is used when the data pattern tends to change at certain time intervals, the Fourier series is used when the data pattern tends to repeat itself, and the kernel is used when the data does not have a specific way. This study aims to obtain parameter estimates for the mixed semiparametric regression model of spline truncated, Fourier series, and the kernel on the biresponse data using the Weighted Least Square (WLS) method. The formed model depends on the selection of knot points, oscillation parameters, and optimal bandwidth. The best model is based on the smallest Generalized Cross Validation (GCV).

Compilation method of CNC lathe cutting force spectrum based on kernel density estimation of G-SCE

The cutting force spectrum of the CNC lathe is the basic data for the reliability design, reliability test, and reliability evaluation of the CNC lathe and its components. Due to the complex and changeable turning conditions and different cutting processes, the cutting load presents multi-peak characteristics. At the same time, grouping the counted load cycles when parameter modeling will produce certain errors. As a result, the parameter distribution model cannot meet the modeling requirements. Thus, a compilation method based on kernel density estimation (KDE) of goodness-smoothness comprehensive evaluation (G-SCE) is proposed. The KDE is used to establish the dynamic cutting force distribution of the CNC lathe in which grouping the counted load cycles is not needed. For the bandwidth-determining methods, the rule of thumb method (ROT) and the least-squares cross-validation method (LCV) do not take into account the influence of different bandwidths on the goodness estimation and the smoothness of the estimated curve, and the G-CSE for KDE is proposed to determining the optimal bandwidth. It includes the estimation accuracy test method based on multiple goodness-of-fit tests and the smoothness test method based on the envelope curve, and the entropy method is used to comprehensively weights the estimated goodness index and the smoothness index to determine the optimal bandwidth. The results of the case analysis indicate that the method proposed can solve the problem of too large estimation error of parameter distribution for multimodal distribution. At the same time, it can better comprehensively evaluate the KDE under different bandwidths. In short, a new method of optimal bandwidth selection is proposed in the original method.

Penerapan Model Geographically Dan Temporally Weighted Regression Pada Kecelakaan Lalu Lintas

Geographically and temporally weighted regression (GTWR) is a model that is used to deal with instability in data both spatially and temporally and to produce local parameters. In this paper, The GTWR model is used to analyze the factors that are thought to significantly influence the number of traffic accidents in Mempawah Regency. The data used in this study came from 8 districts with the variables used were the number of traffic accidents, the number of population (gender ratio, length of damaged road conditions, and percentage of adolescence. The parameter estimation of the GTWR model was obtained using the weighted least square (WLS) method. The optimal bandwidth selection uses the Cross-Validation (CV) method and the weighting used is the Fixed bisquare function. The results of the analysis show that using the GTWR model, it was found that only the population size variable significantly affected the number of traffic accidents in all locations in Mempawah Regency from 2015 to 2018. The GTWR model was known to be better than the multiple regression model because it produced smaller AIC and RSS values and a larger R-square value.

OPTIMAL BANDWIDTH SELECTION IN NONLINEAR COINTEGRATING REGRESSION

We study optimal bandwidth selection in nonparametric cointegrating regression where the regressor is a stochastic trend process driven by short or long memory innovations. Unlike stationary regression, the optimal bandwidth is found to be a random sequence which depends on the sojourn time of the process. All random sequences $h_{n}$ that lie within a wide band of rates as the sample size $n\rightarrow \infty $ have the property that local level and local linear kernel estimates are asymptotically normal, which enables inference and conveniently corresponds to limit theory in the stationary regression case. This finding reinforces the distinctive flexibility of data-based nonparametric regression procedures for nonstationary nonparametric regression. The present results are obtained under exogenous regressor conditions, which are restrictive but which enable flexible data-based methods of practical implementation in nonparametric predictive regressions within that environment.

Does the COVID-19 lockdown improve global air quality? New cross-national evidence on its unintended consequences

Despite a growing literature on the impacts of the COVID-19 pandemic, scant evidence currently exists on its impacts on air quality. We offer an early assessment with cross-national evidence on the causal impacts of COVID-19 on air pollution. We assemble a rich database consisting of daily, sub-national level data of air quality for 164 countries before and after the COVID-19 lockdowns and we analyze it using a Regression Discontinuity Design approach. We find the global concentration of NO2 and PM2.5 to decrease by 5 percent and 4 percent, respectively, using data-driven optimal bandwidth selection. These results are consistent across measures of air quality and data sources and robust to various model specifications and placebo tests. We also find that mobility restrictions following the lockdowns are a possible explanation for improved air quality.

Optimal bandwidth selection for a kernel density with a location-scale property

This paper proposes a novel estimator of the bandwidth in kernel density estimation, built from an adaptive combination of the strengths of classical kernel smoothing and the desirable properties inherent in adjusted kernel smoothing as studied under a variety location and scale family of functions. The optimal bandwidth exists as a function of density functionals derived as the minimizer of the mean square error. We provide a substantial computational assessment of the performance of our proposed estimator on both simulated and real data, and it is very encouraging to notice that our proposed method exhibits a lower variance than its previous counterparts, and also yields an overall smaller mean squared error.

Polarimetric Semivariogram-Based Spatial Scale Selection for PolSAR Image Segmentation With Mean-Shift Algorithm

Image segmentation has been an important procedure in object-based image analysis (OBIA), which takes image object as a processing unit. The spatial scale in image segmentation has great importance in OBIA. Due to the high heterogeneity and large dynamic range of polarimetric synthetic aperture radar (PolSAR) images, it is often difficult to choose optimal spatial scales. This letter proposes a polarimetric semivariogram-based spatial scale selection method for PolSAR image segmentation. The optimal spatial bandwidth parameter in the mean-shift algorithm is pre-estimated based on the combined polarimetric and statistical analysis of PolSAR images. By implementing a quantitative evaluation of segmentation result, the effectiveness of the proposed method in optimal spatial bandwidth selection for PolSAR image segmentation is verified. Experiments on both the EMISAR and UAVSAR L-band PolSAR data sets testify the validity of the proposed adaptive optimal bandwidth selection strategy for PolSAR images.

PUConv: Upsampling convolutional network for point cloud semantic segmentation

Due to the issue of disorder, it is difficult to directly utilise a 2D convolutional neural networks to process 3D point clouds. Recently, PointNet can directly use 3D point sets as the input of convolutional neural networks and complete the processing of point clouds with multi-layer perceptron (MLP) and symmetric functions. However, the use of MLP to compute the weight function ignores the problem of non-uniformity sampling caused by the density of point set data. To address the above problem, based on the PointNet++ structure, a kernel density estimation based method is proposed to calculate the density level of the local point sets region under the optimal bandwidth selection principle, and the density re-weighting of the weight function is developed to better fit the structure of local point clouds. In addition, the authors utilise the upsampling convolution operation to avoid duplicate storages and calculations, making the point cloud reconstruction more efficient. The experiments carried out the semantic segmentation on both the synthetic data and the real indoor scenes show that the proposed method is capable of obtaining promising semantic segmentation results.

Nonparametric Regression with Stochastic Boundary and Regression Discontinuity with Endogenous Cutoff

We augment the usual regression discontinuity design model by considering an endogenously chosen cutoff, perhaps chosen to maximize certain criterion that the treatment provider has. This regime faces the challenge that, conditional on realization of the cutoff, observations are no longer i.i.d. We develop conditions under which an asymptotic expansion of the locally linear estimator contains a bias term caused by the endogeneity of order op(h2 +1/√nh). The lower order bias justifies the usual optimal bandwidth selection and bias correction procedures in this setting, though it places constraints on the maximal degree of undersmoothing.