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The choice of bandwidth is crucial in circular kernel density estimation. Various bandwidth selection techniques have been proposed in the literature. New bandwidth selectors based on the measure β -divergence for kernel density estimation with circular data are presented in this work. These selectors are obtained by minimizing the mean of the measure β -divergence between the density to be estimated and its estimator. The idea is based on the generalization of the standard method which selects the bandwidth by minimizing the mean integrated squared error (MISE). The performance of the proposed selectors is evaluated through a simulation study and compared with other existing selectors. These selectors are illustrated with some real datasets. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Kernel density estimations of circular data are an effective type of nonparametric estimation. The performance of these estimations depends significantly on a smoothing parameter referred to as bandwidth. Selecting suitable bandwidths for these types of estimation pose fundamental challenges, therefore fixed bandwidth selectors are often the initial choice. The study investigates common bandwidth selection methods and proposes novel methods which adopt the idea from the linear case. The attention is also paid to variable bandwidth selection. Using simulations which incorporate a range of circular distributions that exhibit multimodality, peakedness and skewness, the proposed methods were evaluated and then compared with other bandwidth selectors to determine their potential advantages. Two real datasets, one containing animal movements and the other wind direction data, were applied to illustrate the utility of the proposed methods. [ABSTRACT FROM AUTHOR]

This work presents the symbol error rate (SER) and outage probability analysis of multi-layer unmanned aerial vehicles (UAVs) wireless communications assisted by intelligent reflecting surfaces (IRS). In such systems, the UAVs may experience high jitter, making the estimation and compensation of the end-to-end phase for each propagation path prone to errors. Consequently, the imperfect phase knowledge at the IRS should be considered. The phase error is modeled using the von Mises distribution and the analysis is performed using the Sinusoidal Addition Theorem (SAT) to provide accurate results when the number of reflectors $L\leq 3$ , and the Central Limit Theorem (CLT) when $L\geq 4$. The achieved results show that accurate phase estimation is critical for IRS based systems, particularly for a small number of reflecting elements. For example, the SER at 10−3 degrades by about 5 dB when the von Mises concentration parameter $\kappa =2$ and $L=30$ , but the degradation for the same $\kappa $ surges to 25 dB when $L=2$. The air-to-air (A2A) channel for each propagation path is modeled as a single dominant line-of-sight (LoS) component, and the results are compared to the Rician channel. The obtained results reveal that the considered A2A model can be used to accurately represent the A2A channel with Rician fading. [ABSTRACT FROM AUTHOR]

We introduce a class of local likelihood circular density estimators, which includes the kernel density estimator as a special case. The idea lies in optimizing a spatially weighted version of the log-likelihood function, where the logarithm of the density is locally approximated by a periodic polynomial. The use of von Mises density functions as weights reduces the computational burden. Also, we propose closed-form estimators which could form the basis of counterparts in the multidimensional Euclidean setting. Simulation results and a real data case study are used to evaluate the performance and illustrate the results. [ABSTRACT FROM AUTHOR]

Local likelihood has been mainly developed from an asymptotic point of view, with little attention to finite sample size issues. The present paper provides simulation evidence of how likelihood density estimation practically performs from two points of view. First, we explore the impact of the normalization step of the final estimate, second we show the effectiveness of higher order fits in identifying modes present in the population when small sample sizes are available. We refer to circular data, nevertheless it is easily seen that our findings straightforwardly extend to the Euclidean setting, where they appear to be somehow new. [ABSTRACT FROM AUTHOR]

Measuring the quality of determined protein structures is a very important problem in bioinformatics. Kernel density estimation is a well-known nonparametric method which is often used for exploratory data analysis. Recent advances, which have extended previous linear methods to multi-dimensional circular data, give a sound basis for the analysis of conformational angles of protein backbones, which lie on the torus. By using an energy test, which is based on interpoint distances, we initially investigate the dependence of the angles on the amino acid type. Then, by computing tail probabilities which are based on amino-acid conditional density estimates, a method is proposed which permits inference on a test set of data. This can be used, for example, to validate protein structures, choose between possible protein predictions and highlight unusual residue angles. [ABSTRACT FROM PUBLISHER]

Abstract: Kernel density estimation for multivariate, circular data has been formulated only when the sample space is the sphere, but theory for the torus would also be useful. For data lying on a d-dimensional torus , we discuss kernel estimation of a density, its mixed partial derivatives, and their squared functionals. We introduce a specific class of product kernels whose order is suitably defined in such a way to obtain L 2-risk formulas whose structure can be compared to their Euclidean counterparts. Our kernels are based on circular densities; however, we also discuss smaller bias estimation involving negative kernels which are functions of circular densities. Practical rules for selecting the smoothing degree, based on cross-validation, bootstrap and plug-in ideas are derived. Moreover, we provide specific results on the use of kernels based on the von Mises density. Finally, real-data examples and simulation studies illustrate the findings. [Copyright &y& Elsevier]