Bandwidth Selection Research Articles

Multiscale geographically weighted quantile regression

ABSTRACT Spatial heterogeneity across multiple scales is a common issue in various disciplines including economics and public health. Geographically weighted quantile regression (GWQR) addresses this by assuming the same spatial scale for all modelled processes at each quantile. This paper introduces a multiscale geographically weighted quantile regression (MGWQR) that allows different processes to operate at different spatial scales at each quantile across the entire response distribution. The methodology estimates optimal bandwidths at each quantile of the response distribution using a back-fitting algorithm, with the selection of bandwidths done within the algorithm using the golden search optimisation method. Simulation study and a real-world example, that considers analysing the impacts of a set of socioeconomic and climate variables on children’s stunting, show that MGWQR outperforms GWQR and QR models.

Bandwidth selection in kernel M-estimation of regression function with truncated, censored and dependent data

Based on randomly left truncated and right censored (LTRC) data, we investigate the problem of selecting an appropriate bandwidth, for the Robust smooth M-estimator m ̂ ( . ) of the regression function m ( . ) , under strong mixing condition. We show that the local ( h loc ( x ) ) and the global ( h glob ) bandwidths obtained as the minimizers of the MSE and the MISE distances, respectively, are asymptotically optimal for m ̂ ( . ) . As a consequence, a bandwidth selector based on plug-in ideas is introduced. We also present a robust version of the Cross-Validation (RCV) bandwidth selection as an alternative to the plug-in method. A simulation study is performed to examine and compare the practical performance of both two methods. Furthermore, these methodologies are applied to a real data problem with the aim of predicting times to death of AIDS cases.

Bandwidth Selection for Large Covariance and Precision Matrices

Bandwidth Selection for Large Covariance and Precision Matrices

A Simple Single‐Layer Wideband Filtenna With Multiple Controllable Radiation Nulls

ABSTRACTIn this letter, a single‐layer wideband filtenna with multiple controllable radiation nulls is presented. The developed filtenna has a very simple structure and is composed with a square substrate integrated waveguide (SIW) cavity, a square patch, and a pair of U‐shaped slots. Notably, the filtenna possesses three radiation nulls that can be tuned by adjusting specific geometrical parameters. To achieve a wide bandwidth and better frequency selectivity, the TM10 mode of the square patch is utilized to couple with the TE210 mode of the square SIW cavity. And a radiation null at upper and lower edge of the passband can be simultaneously obtained because of the effective multipath coupling and the impact of TE110 mode in SIW cavity. An extra in‐band resonance and out‐of‐band radiation null are concurrently introduced by etching a pair of U‐shaped slots at the metal ground plane so as to further expand the bandwidth and enhance the frequency selectivity. To validate the design method, a prototype of the filtenna operating at center frequency of 4.76 GHz was fabricated and measured. The measurement results show an impedance fractional bandwidth of 15.8% (4.38‐5.13 GHz) and a peak realized gain of 6.1dBi.

On the calibration of multiscale geographically and temporally weighted regression models

Spatiotemporal analysis and modeling have long been key foci of geographical information science. In a recent paper, Wu et al. expanded the local spatial modeling technique of multiscale geographically weighted regression (MGWR) to incorporate a temporal component. This new model is named multiscale geographically and temporally weighted regression (MGTWR). Despite the utility of expanding MGWR to incorporate a temporal weighting function in addition to the existing spatial one, the approach developed by Wu et al. has two limitations: the bandwidth selection algorithm cannot guarantee an optimal result and no formulation for the effective number of parameters (ENPs) in the model is given. To address these issues, this paper describes a procedure to derive an optimal temporal and an optimal spatial bandwidth for MGTWR and also develops a formula for the ENPs in the model. The former ensures the reliability of the model outputs while the latter is essential for making reliable inferences from the local parameter estimates generated in the calibration of models by MGTWR. These advances in the MGTWR framework are demonstrated through applications to simulated and real-world data.

A bootstrap-based bandwidth selection rule for kernel quantile estimators

A bootstrap-based bandwidth selection rule for kernel quantile estimators

Bandwidth selection methods for non parametric regression with spatially correlated data

. In non parametric regression estimation, a critical and unavoidable step is to choose the smoothing parameters (bandwidth) to control the smoothness of the curve estimate. In the presence of spatially correlated errors, the traditional data-driven bandwidth selection methods, such as cross-validation and generalized cross-validation, do not work well for providing efficient bandwidth values. Moreover, the existing methods are based on estimation of correlation structure. As errors are unobservable, estimation of correlation is a big challenge. This article studies bandwidth selection methods for local linear regression (LLR) in the presence of correlated errors. For this purpose, we derive the weighted mean average square errors (WMASE) and use it along with bias-correlated generalized cross-validation (GCV) as bandwidth selection criterion. We then get the estimates of bandwidth by two ways: by minimizing the weighted mean average square errors (WMASE) and by using the bias-correlated generalized cross-validation (GCV) criterion. Due to its good properties, the composite likelihood (CL) is used to estimate the correlation. The results show that composite likelihood provides better estimates than maximum likelihood (ML) in the sense of producing more reasonable estimates of correlation parameters and bandwidth values. Also, our methods appear reasonably robust to the misspecification of the parametric correlation model. Moreover, the proposed methods work much better than ignoring the correlation and applying traditional methods. Finally, we apply our methods on water chemistry data collected about lakes in the Northeastern United States.

Uniform in Number of Neighbor Consistency and Weak Convergence of k-Nearest Neighbor Single Index Conditional Processes and k-Nearest Neighbor Single Index Conditional U-Processes Involving Functional Mixing Data

U-statistics are fundamental in modeling statistical measures that involve responses from multiple subjects. They generalize the concept of the empirical mean of a random variable X to include summations over each m-tuple of distinct observations of X. W. Stute introduced conditional U-statistics, extending the Nadaraya–Watson estimates for regression functions. Stute demonstrated their strong pointwise consistency with the conditional expectation r(m)(φ,t), defined as E[φ(Y1,…,Ym)|(X1,…,Xm)=t] for t∈Xm. This paper focuses on estimating functional single index (FSI) conditional U-processes for regular time series data. We propose a novel, automatic, and location-adaptive procedure for estimating these processes based on k-Nearest Neighbor (kNN) principles. Our asymptotic analysis includes data-driven neighbor selection, making the method highly practical. The local nature of the kNN approach improves predictive power compared to traditional kernel estimates. Additionally, we establish new uniform results in bandwidth selection for kernel estimates in FSI conditional U-processes, including almost complete convergence rates and weak convergence under general conditions. These results apply to both bounded and unbounded function classes, satisfying certain moment conditions, and are proven under standard Vapnik–Chervonenkis structural conditions and mild model assumptions. Furthermore, we demonstrate uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. This result is independently valuable and has potential applications in areas such as set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and discrimination problems.

Local linear estimators for reflected diffusions

In this paper, we investigate the nonparametric local linear estimator for the drift function of reflected stochastic differential equations based on the discretely observed process. Under certain regularity conditions, we prove the strong consistency and establish the asymptotic normality for our proposed estimator. We also propose the optimal bandwidth selector for the estimator and show that the estimator does not have a boundary effect. Simulation results demonstrate that our method is superior to the method proposed by Cholaquidis et al. [Stat. Sin. 2021, 31: 29–51]. We apply the EUR/USD currency exchange rate data to illustrate our theoretical results.

Modal volatility function

We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias.

Assessing wind energy exploitation potential in several regions of Viet Nam using Kernel density estimation model

This article analyzes and assesses the potential for wind energy exploitation in six regions of Vietnam. The wind speed data are used to construct wind speed probability distributions (WSPDs) based on kernel density estimation (KDE). The KDE distribution, with six bandwidth selection methods, is implemented to generate probability density functions (PDFs) for each region's data to describe wind speed characteristics. The statistical tests Cramér-Von Mises (CvM), Anderson-Darling (A-D), and Kolmogorov-Smirnov (K-S) are applied to evaluate the PDFs' goodness-of-fit performance. The analysis results present the KDE distribution using the least-squares cross-validation (LSCV), and the Scott bandwidth selection method has outstanding fitting performance. Based on these PDF distributions, the wind turbine (WT) power curve is used to estimate and predict the amount of electricity that can be produced. This study also proposes a reliable method for wind power output planning based on wind speed that can be universally applied.

Adaptive extraction of characteristic ridges from time-frequency representation for wheelset bearings failure diagnosis under time-varying speed

Instantaneous frequencies-based order tracking is an excellent approach for bearing faults diagnosing at time-varying speeds. The key is to extract ridges from time-frequency representation. However, their precision seriously relies on the cost function and bandwidth selection. To address these issues, an adaptive extraction of characteristic ridges (AECR) method that integrates a variable-bandwidth ridge edge detection (VBRED) and an adaptive exponential cost function (AECF) is presented. VBRED provides a variable-bandwidth search area-based clustering algorithm to isolate neighboring components. AECF can be automatically adjusted based on the signal signature to ensure the smoothness of the ridge. The average frequency ratios of the extracted ridges are used to identify the health conditions of the bearings. Finally, the effectiveness of the proposed AECR is validated by simulations and experiments. The results prove that it performs excellently when the energy and relative position of the ridges are close, compared to other state-of-the-art methods.

Geographically weighted accelerated failure time model for spatial survival data: application to ovarian cancer survival data in New Jersey

BackgroundIn large multiregional cohort studies, survival data is often collected at small geographical levels (such as counties) and aggregated at larger levels, leading to correlated patterns that are associated with location. Traditional studies typically analyze such data globally or locally by region, often neglecting the spatial information inherent in the data, which can introduce bias in effect estimates and potentially reduce statistical power.MethodWe propose a Geographically Weighted Accelerated Failure Time Model for spatial survival data to investigate spatial heterogeneity. We establish a weighting scheme and bandwidth selection based on quasi-likelihood information criteria. Theoretical properties of the proposed estimators are thoroughly examined. To demonstrate the efficacy of the model in various scenarios, we conduct a simulation study with different sample sizes and adherence to the proportional hazards assumption or not. Additionally, we apply the proposed method to analyze ovarian cancer survival data from the Surveillance, Epidemiology, and End Results cancer registry in the state of New Jersey.ResultsOur simulation results indicate that the proposed model exhibits superior performance in terms of four measurements compared to existing methods, including the geographically weighted Cox model, when the proportional hazards assumption is violated. Furthermore, in scenarios where the sample size per location is 20-25, the simulation data failed to fit the local model, while our proposed model still demonstrates satisfactory performance. In the empirical study, we identify clear spatial variations in the effects of all three covariates.ConclusionOur proposed model offers a novel approach to exploring spatial heterogeneity of survival data compared to global and local models, providing an alternative to geographically weighted Cox regression when the proportional hazards assumption is not met. It addresses the issue of certain counties' survival data being unable to fit the model due to limited samples, particularly in the context of rare diseases.

Grid Point Approximation for Distributed Nonparametric Smoothing and Prediction

Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we find that the popularly used one-shot type estimator is highly inefficient for prediction purposes. To this end, we propose a novel grid point approximation (GPA) method, which has the following advantages. First, the resulting GPA estimator is as statistically efficient as the global estimator under mild conditions. Second, it requires no communication and is extremely efficient in terms of computation for prediction. Third, it is applicable to the case where the data are not randomly distributed across different machines. To select a suitable bandwidth, two novel bandwidth selectors are further developed and theoretically supported. Extensive numerical studies are conducted to corroborate our theoretical findings. Two real data examples are also provided to demonstrate the usefulness of our GPA method.

Rational-quadratic kernel-based maximum correntropy Kalman filter for the non-Gaussian noises

In this paper, a rational-quadratic kernel-based maximum correntropy Kalman filter (RKMCKF) algorithm is proposed to improve the estimation accuracy for non-Gaussian noise interference. Firstly, the RKMCKF algorithm is derived to eliminate the singular matrix produced by multi-dimensional non-Gaussian noise disturbance. Secondly, the upper limit is analyzed to provide a theoretical range for kernel bandwidth, which is beneficial for the selection of proper kernel bandwidths and boosting the precision of state estimation. Furthermore, the boundness of the state estimation error is verified to manifest the RKMCKF algorithm stability. Finally, under different types of non-Gaussian noise, the proposed RKMCKF algorithm is demonstrated to promote the accuracy of state estimation compared with the conventional Kalman filter, Gaussian sum filter, Huber filter, and maximum correntropy Kalman filter through the simulations.

A comprehensive exploration of complete cross-validation for circular data

Kernel density estimation of circular data has recently received considerable attention for its ability to model and analyse distributions on unit circles and other periodic domains. Our aim is to contribute to the literature on data-driven bandwidth selectors in circular kernel density estimation. We propose a novel circular-specific method that is based on a crossvalidation procedure with a von Mises density used as a kernel function. Using simulated data as well as real-world circular datasets, we evaluate and validate the proposed method and compare it with the existing methods.

Nonparametric conditional survival function estimation and plug-in bandwidth selection with multiple covariates

Nonparametric conditional survival function estimation and plug-in bandwidth selection with multiple covariates

Polarization-insensitive cross-polarization converter with high frequency selectivity based on an antenna-resonator-antenna module

In this paper, a novel transmission-type polarization-insensitive frequency selective polarization converter (PIFSPC) is proposed. The overall structural scheme of the proposed PIFSPC is based on an antenna-resonator-antenna (ARA) module, which is composed of a receiving patch antenna, double “S-shaped” half-wavelength resonators, and a transmitting patch antenna. By adopting cross-coupling, high frequency selectivity is achieved, and through the utilization of a staggered rotationally symmetric structure, polarization insensitivity is attained. The prototype possesses four transmission poles and two zeros on the polarization conversion spectrum, and it shows insensitivity to the polarization direction of incident electromagnetic waves. The frequency selectivity of the prototype at the lower and upper band edges is 425 dB/GHz and 283 dB/GHz respectively. The cross-polarization conversion rate (PCR) is over 95% within the passband from 4.93 GHz to 5.09 GHz for arbitrarily polarized azimuth incident waves, and its thickness is merely 0.052λ0. The operation bandwidth and frequency selectivity of the prototype can be readily altered. A prototype is fabricated and measured, with excellent consistency between simulations and experiments. It indicates the feasibility of integrating frequency selection and polarization conversion. The proposed PIFSPC has extensive application prospects in enhancing the anti-interference ability and electromagnetic compatibility in the fields of communication, measurement, and microwave detection.

Robust tests for equality of regression curves based on characteristic functions

This paper focuses on the problem of testing the null hypothesis that the regression functions of several populations are equal under a general nonparametric homoscedastic regression model. It is well known that linear kernel regression estimators are sensitive to atypical responses. These distorted estimates will influence the test statistic constructed from them so the conclusions obtained when testing equality of several regression functions may also be affected. In recent years, the use of testing procedures based on empirical characteristic functions has shown good practical properties. For that reason, to provide more reliable inferences, we construct a test statistic that combines characteristic functions and residuals obtained from a robust smoother under the null hypothesis. The asymptotic distribution of the test statistic is studied under the null hypothesis and under root − n contiguous alternatives. A Monte Carlo study is performed to compare the finite sample behaviour of the proposed test with the classical one obtained using local averages. The reported numerical experiments show the advantage of the proposed methodology over the one based on Nadaraya–Watson estimators for finite samples. An illustration to a real data set is also provided and enables to investigate the sensitivity of the p − value to the bandwidth selection.

Analysis of Regression Discontinuity Designs with a Binary Moderating Variable

Regression discontinuity (RD) designs are increasingly used for causal evaluations. However, the literature contains little guidance for conducting a moderation analysis within an RDD context. The current article focuses on moderation with a single binary variable. A simulation study compares: (1) different bandwidth selectors and (2) local polynomial regressions with interactions to local regressions on subsets of the data defined by values of the moderating variable. We find that existing bandwidth selectors optimized for main effects will choose bandwidths that are too small for moderation analysis. Additionally, choosing an optimal bandwidth for the subset regression approach may not be feasible for small to moderate sample sizes unless the moderator prevalence is near 0.5 and correlation with the assignment variable is small. We conclude that when sample sizes are small a global regression approach is likely to be preferred to utilizing bandwidth selectors optimized for main effects.