Bandwidth Selection Research Articles

A Comparative Study of Higher Order Kernel Estimation and Kernel Density Derivative Estimation of the Gaussian Kernel Estimator with Data Application

Higher-order kernel estimation and kernel density derivative estimation are techniques for reducing the asymptotic mean integrated squared error in nonparametric kernel density estimation. A reduction in the error criterion is an indication of better performance. The estimation of kernel function relies greatly on bandwidth and the identified reduction methods in the literature are bandwidths reliant for their implementation. This study examines the performance of higher order kernel estimation and kernel density derivatives estimation techniques with reference to the Gaussian kernel estimator owing to its wide applicability in real-life-settings. The explicit expressions for the bandwidth selectors of the two techniques in relation to the Gaussian kernel and the bandwidths were accurately obtained. Empirical results using two data sets obviously revealed that kernel density derivative estimation outperformed the higher order kernel estimation excellently well with the asymptotic mean integrated squared error as the criterion function.

Wideband Low-Loss Filter With Compact Size and Wide Stopband Based on Folded Planar Waveguide

In this letter, a hybrid, compact doubly slot-loaded folded ridged half-mode substrate-integrated waveguide (FRHMSIW) filter with wide bandwidth and high selectivity is presented and investigated. The low-pass and high-pass cutoff frequencies of the wideband filter can be independently controlled by adjusting the dimensions of the quasi-periodic slots and FRHMSIW sections, respectively. The dispersion curves, surface current distribution, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E$</tex-math> </inline-formula> -field vector diagram of the proposed hybrid FRHMSIW bandpass unit are illustrated. Parametric study and loss analysis are also conducted. The footprint of the proposed filter is miniaturized due to the upper-side-slot-loaded FRHSIW transmission structure and meandered middle-layer slots. The stopband is further extended by etching I-shaped patterns on the ground layer. Finally, the filter is designed, simulated, and measured, with a wide passband between 3.86 and 8.3 GHz, a minimum insertion loss of 0.56 dB, a rejection level better than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-$</tex-math> </inline-formula> 20 dB from 8.6 to 20.8 GHz, and an electrical size of only 0.21 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda _{g}^{2}$</tex-math> </inline-formula> at the center frequency.

IBAC: An Intelligent Dynamic Bandwidth Channel Access Avoiding Outside Warning Range Problem

IEEE 802.11ax uses the concept of primary and secondary channels, leading to the Dynamic Bandwidth Channel Access (DBCA) mechanism. By applying DBCA, a wireless station can select a wider channel bandwidth, such as 40/80/160 MHz, by applying the channel bonding feature. However, during channel bonding, inappropriate bandwidth selection can cause collisions. Therefore, to avoid collisions, a well-developed media access control (MAC) protocol is crucial to effectively utilize the channel bonding mechanism. In this paper, we address a collision scenario, called Outside Warning Range Problem (OWRP), that may occur during DBCA when a wireless station interferes with another wireless station after channel bonding is performed. Therefore, we propose a MAC layer mechanism, Intelligent Bonding Avoiding Collision (IBAC), that adapts the channel bonding level in DBCA in order to avoid the OWRP. We first design a theoretical model based on Markov chains for DBCA while avoiding the OWRP. Based on this model, we design a Thompson sampling based Bayesian approach to select the best possible channel bonding level intelligently. We analyze the performance of the IBAC through simulations where it is observed that, comparing to other competing mechanisms, the proposed approach can enhance the network performance significantly while avoiding the OWRP.

Mean group instrumental variable estimation of time-varying large heterogeneous panels with endogenous regressors

The large heterogeneous panel data models are extended to the setting where the heterogenous coefficients are changing over time and the regressors are endogenous. Kernel-based non-parametric time-varying parameter instrumental variable mean group (TVP-IV-MG) estimator is proposed for the time-varying cross-sectional mean coefficients. The uniform consistency is shown and the pointwise asymptotic normality of the proposed estimator is derived. A data-driven bandwidth selection procedure is also proposed. The finite sample performance of the proposed estimator is investigated through a Monte Carlo study and an empirical application on multi-country Phillips curve with time-varying parameters.

A novel MIMO antenna with switchable UWB/5G modes for vehicular terminals

AbstractThis paper demonstrates the design and development of a dual‐operating mode multiple‐input and multiple‐output (MIMO) antenna. The MIMO antenna comprises a novel ultrawideband (UWB) antenna with selectively chosen feedlines to obtain bandwidth reconfiguration. The novel UWB monopole evolved from a rectangular monopole whose radiating portion and the ground plane are shaped to obtain broadband impedance matching from 2.3 to 10.7 GHz (Mode 1). The antenna is excited using a 50‐Ω microstrip line. An additional feed path is created and deployed to achieve bandwidth selectivity with a tuning fork bandpass filter (BPF) operating between 2.8 and 4 GHz. Bandwidth selection is performed using a pair of positive–intrinsic–negative diodes. Thus, in the reconfigured state, the monopole is connected to the excitation source through the BPF, restricting the operational bandwidth to 2.8–4.0 GHz (Mode 2). A vertically polarized four‐element MIMO antenna with pattern diversity characteristics is constructed, and the performance parameters are studied. The proposed multiantenna is fabricated and tested in the laboratory. The proposed MIMO antenna offers a measured gain of over 3.51 dBi and total efficiency above 78%. The proposed multielement antenna is suitable for UWB communications, including ISM, LTE2700, and sub‐6 GHz 5G communications at 3.5 GHz in the vehicular environment.

Dingo optimization based network bandwidth selection to reduce processing time during data upload and access from cloud by user

Dingo optimization based network bandwidth selection to reduce processing time during data upload and access from cloud by user

Regularised Semi-parametric Composite Likelihood Intensity Modelling of a Swedish Spatial Ambulance Call Point Pattern

Motivated by the development of optimal dispatching strategies for prehospital resources, we model the spatial distribution of ambulance call events in the Swedish municipality Skellefteå during 2014–2018 in order to identify important spatial covariates and discern hotspot regions. Our large-scale multivariate data point pattern of call events consists of spatial locations and marks containing the associated priority levels and sex labels. The covariates used are related to road network coverage, population density, and socio-economic status. For each marginal point pattern, we model the associated intensity function by means of a log-linear function of the covariates and their interaction terms, in combination with lasso-like elastic-net regularized composite/Poisson process likelihood estimation. This enables variable selection and collinearity adjustment as well as reduction of variance inflation from overfitting and bias from underfitting. To incorporate mobility adjustment, reflecting people’s movement patterns, we also include a nonparametric (kernel) intensity estimate as an additional covariate. The kernel intensity estimation performed here exploits a new heuristic bandwidth selection algorithm. We discover that hotspot regions occur along dense parts of the road network. A mean absolute error evaluation of the fitted model indicates that it is suitable for designing prehospital resource dispatching strategies. Supplementary materials accompanying this paper appear online.

Automatic Clustering and Classification of Coffee Leaf Diseases Based on an Extended Kernel Density Estimation Approach.

The current methods of classifying plant disease images are mainly affected by the training phase and the characteristics of the target dataset. Collecting plant samples during different leaf life cycle infection stages is time-consuming. However, these samples may have multiple symptoms that share the same features but with different densities. The manual labelling of such samples demands exhaustive labour work that may contain errors and corrupt the training phase. Furthermore, the labelling and the annotation consider the dominant disease and neglect the minor disease, leading to misclassification. This paper proposes a fully automated leaf disease diagnosis framework that extracts the region of interest based on a modified colour process, according to which syndrome is self-clustered using an extended Gaussian kernel density estimation and the probability of the nearest shared neighbourhood. Each group of symptoms is presented to the classifier independently. The objective is to cluster symptoms using a nonparametric method, decrease the classification error, and reduce the need for a large-scale dataset to train the classifier. To evaluate the efficiency of the proposed framework, coffee leaf datasets were selected to assess the framework performance due to a wide variety of feature demonstrations at different levels of infections. Several kernels with their appropriate bandwidth selector were compared. The best probabilities were achieved by the proposed extended Gaussian kernel, which connects the neighbouring lesions in one symptom cluster, where there is no need for any influencing set that guides toward the correct cluster. Clusters are presented with an equal priority to a ResNet50 classifier, so misclassification is reduced with an accuracy of up to 98%.

Optimal minimax rates of specification testing with data-driven bandwidth

This study investigates optimal minimax rates of specification testing for linear and non-linear instrumental variable regression models. The test constructed by non-parametric kernel techniques can be rate optimal when bandwidths are selected appropriately. Since bandwidths are often selected in a data-dependent way in empirical studies, the rate-optimality of the test with data-driven bandwidths is investigated. While least squares cross-validation selects bandwidths that are optimal for estimation, it is shown not to be optimal for testing. Thus, we propose a novel bandwidth selection method for testing, the performance of which is investigated in a simulation study.

Optimum adaptive bandwidth selection method of local fitting in kernel regression analysis for non-uniform data

Optimum adaptive bandwidth selection method of local fitting in kernel regression analysis for non-uniform data

Intelligent Fault Detection for Rotating Machinery Using Cyclic Morphological Modulation Spectrum and Hierarchical Teager Permutation Entropy

Intelligent fault detection of rotating machines is essentially a pattern classification issue. At the same time, effectively obtaining fault features from the measured signals is a key step to timely diagnose the health status of rotating machinery and evaluate the results of fault classification. To accurately obtain effective fault information to enhance fault accuracy, this paper proposes a novel fault detection scheme based on cyclic morphological modulation spectrum (CMMS) and hierarchical Teager permutation entropy (HTPE). In this scheme, firstly, CMMS was developed to analyze the measured signal to obtain a series of CMMS slices with different frequency bands, which solved the deficiencies of manual empirical selection of frequency band bandwidth in the traditional cyclic modulation spectrum (CMS). Subsequently, by integrating Teager energy operator into hierarchical permutation entropy (HPE), an improved feature selection method named hierarchical Teager permutation entropy (HTPE) is presented to obtain fault information of different frequency band slices, which can improve the fault feature extraction capability of HPE. Finally, the acquired HTPE-based vectors are integrated into the extreme learning machine (ELM) classifier to achieve fault classification of rotating machinery under different working conditions. The proposed scheme is validated by experimental cases including cylindrical roller bearings and planetary gearboxes. The analysis results indicate that the proposed scheme not only can effectively obtain the fault features, but also accurately realize the classification and recognition of the fault mode. In addition, the proposed scheme can achieve higher detection accuracy than some existing algorithms.

Novel Unbalanced-to-Balanced Quad-Channel Diplexer With Controllable Bandwidth and High Isolation

A novel unbalanced-to-balanced (UBTB) quad- channel diplexer consisting of two balun filters sharing a common single-ended microstrip feeder is proposed. By loading a stepped-impedance quad-mode resonator (SIQMR) into the balun filter, not only each mode can be flexibly adjusted, but also the size of the circuit can be reduced. In addition, motivated by the internal hybrid coupling, two adjacent modes are utilized to form a passband filter with a transmission zero. On the basis of which, two channels with flexibly adjustable bandwidth and good frequency selectivity are implemented on Rx or Tx path. Finally, a U-shaped microstrip slot-line structure is utilized as the balanced port to achieve good common-mode (CM) suppression. To verify the proposed diplexer, a quad-channel prototype is designed, fabricated and tested. Measured results of the fabricated circuit agree well with the simulated ones.

Robust nonparametric regression: Review and practical considerations

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have been proposed in the literature, most of them can be highly sensitive to the presence of a small proportion of atypical observations in the training set. A review of outlier robust estimation methods for nonparametric regression models is provided, paying particular attention to practical considerations. Since outliers can also influence negatively the regression estimator by affecting the selection of bandwidths or smoothing parameters, a discussion of robust alternatives for this task is also included. Using many of the “classical” nonparametric regression estimators (and their robust counterparts) can be very challenging in settings with a moderate or large number of explanatory variables, so recently proposed robust nonparametric regression methods that scale well with a growing number of covariates are also discussed.

Fast Selection of Bandwidths for Nonparametric Estimation of the Probability Density of a Two-Dimensional Random Variable with Dependent Components

Fast Selection of Bandwidths for Nonparametric Estimation of the Probability Density of a Two-Dimensional Random Variable with Dependent Components

Nonparametric goodness-of-fit testing for a continuous multivariate parametric model

A novel goodness-of-fit test of a continuous parametric model in the multivariate setting, based on aggregating local discrepancies between a nonparametric estimate of the density and the parametrically estimated density under the null model, is introduced. The theoretical results of the article include analytic quantification of the test statistic’s asymptotic distribution under both the null and alternative hypotheses, including closed-form expressions for its asymptotic power under fixed and local alternatives. Motivated by a Berry–Esseen type bound that we derive, a bandwidth selector which optimizes a measure of the test statistic’s rate of convergence to normality is introduced. A bootstrap size function approximation yields cut-off points suitable for finite sample implementations of the test. An extensive simulation study under Pitman and Kullback–Leibler alternatives compares the new test to well-established tests in the literature and demonstrates the strong and competitive performance of the former in the majority of the examples considered. Finally, the practical usefulness of the new test is demonstrated in the analysis of a real dataset involving stock market returns.

Bandwidth selection for nonparametric regression with errors-in-variables

We propose two novel bandwidth selection procedures for the nonparametric regression model with classical measurement error in the regressors. Each method evaluates the prediction errors of the regression using a second (density) deconvolution. The first approach uses a typical leave-one-out cross-validation criterion, while the second applies a bootstrap approach and the concept of out-of-bag prediction. We show the asymptotic validity of both procedures and compare them to the SIMEX method in a Monte Carlo study. As well as dramatically reducing computational cost, the methods proposed in this article lead to lower mean integrated squared error (MISE) compared to the current state-of-the-art.

Confidence intervals for the length of the receiver-operating characteristic curve based on a smooth estimator.

A good diagnostic test should show different behavior on both the positive and the negative populations. However, this is not enough for having a good classification system. The binary classification problem is a complex task, which implies to define decision criteria. The knowledge of the level of dissimilarity between the two involved distributions is not enough. We also have to know how to define those decision criteria. The length of the receiver-operating characteristic curve has been proposed as an index of the optimal discriminatory capacity of a biomarker. It is related not with the actual but with the optimal classification capacity of the considered diagnostic test. One particularity of this index is that its estimation should be based on parametric or smoothed models. We explore here the behavior of a kernel density estimator-based approximation for estimating the length of the receiver-operating characteristic curve. We prove the asymptotic distribution of the resulting statistic, propose a parametric bootstrap algorithm for confidence intervals construction, discuss the role that the bandwidth parameter plays in the quality of the provided estimations and, via Monte Carlo simulations, study its finite-sample behavior considering four different criteria for the bandwidth selection. The practical use of the length of the receiver-operating characteristic curve is illustrated through two real-world examples.

Kernel Estimation of Bivariate Time-Varying Coefficient Model for Longitudinal Data with Terminal Event

We propose a nonparametric bivariate time-varying coefficient model for longitudinal measurements with the occurrence of a terminal event that is subject to right censoring. The time-varying coefficients capture the longitudinal trajectories of covariate effects along with both the followup time and the residual lifetime. The proposed model extends the parametric conditional approach given terminal event time in recent literature, and thus avoids potential model misspecification. We consider a kernel smoothing method for estimating regression coefficients in our model and use cross-validation for bandwidth selection, applying undersmoothing in the final analysis to eliminate the asymptotic bias of the kernel estimator. We show that the kernel estimates follow a finite-dimensional normal distribution asymptotically under mild regularity conditions, and provide an easily computed sandwich covariance matrix estimator. We conduct extensive simulations that show desirable performance of the proposed approach, and apply the method to analyzing the medical cost data for patients with end-stage renal disease. Supplementary materials for this article are available online.

Bandwidth selection for kernel density estimation of fat-tailed and skewed distributions

Applied researchers using kernel density estimation have worked with optimal bandwidth rules that invariably assumed that the reference density is Normal (optimal only if the true underlying density is Normal). We offer four new optimal bandwidth rules-of-thumb based on other infinitely supported distributions: Logistic, Laplace, Student's t and Asymmetric Laplace. Additionally, we propose a psuedo rule-of-thumb (ROT) bandwidth based on a Gram-Charlier expansion of the unknown reference density that is linked to the empirical skewness and kurtosis of the data. The intellectual investment needed to implement these new optimal bandwidths is practically zero. We discuss the behaviour of these bandwidths as it links to differences in skewness and kurtosis to the Normal reference ROT. We further propose model selection criteria for bandwidth choice when the true underlying density is unknown. The performance of these new ROT bandwidths are assessed in a variety of Monte Carlo simulations as well as in two empirical illustrations, the well known data set of annual snowfall in Buffalo, New York, and a timely example on stock market trading.

A single‐layer differential‐fed dual‐band filtering antenna for WLAN application

AbstractIn this letter, a single‐layer differential‐fed dual‐band filtering antenna for wireless local area network application is proposed. The proposed antenna consists of a square patch, and two pairs of stepped impedance resonators (SIRs). The lower operating passband is realized by exciting the square patch with a pair of differential ports. Then, a pair of SIRs is connected with the radiating edge of the square patch to introduce another resonance, thus forming the upper passband. And a radiation null is simultaneously produced to enhance the frequency selectivity between the two passbands. Moreover, another pair of SIRs is utilized to connect with the nonradiating edge of the square patch, which generates an additional high‐frequency in‐band resonance and a radiation null to further improve the bandwidth and frequency selectivity of upper passband. The developed prototype was fabricated and measured to verify the design concept. The measured results are in good agreement with the simulated ones, demonstrating that it exhibits −10 dB fractional impedance bandwidths of 3.68% and 7.35%, maximum realized gains at boresight direction of 5.5 and 8.7 dBi, and cross‐polarization levels smaller than −30 dB, in lower and upper passbands, respectively.