Bandwidth selection for kernel density estimation using Fourier domain constraints

Kernel density estimation (KDE) is widely-used for non-parametric estimation of an underlying density from data. The performance of KDE is mainly dependent on the bandwidth parameter of the kernel. This study presents an alternative method of estimating the bandwidth by incorporating sparsity priors in the Fourier transform domain. By using cross-validation (CV) together with an l1 constraint, the proposed method significantly reduces the under-smoothing effect of traditional CV methods. A solution for all free parameters in the minimisation is proposed, such that the algorithm does not need any additional parameter tuning. Simulation results indicate that the new approach is able to outperform classical and more recent approaches over a set of distributions of interest. © The Institution of Engineering and Technology

A New Multivariate Product Kernel Functions of the Beta Polynomial Family

Multivariate analysis of data is of wide applicability in data science especially in big data analytic due to the volume of concealed information to be analyzed. Accurate analysis of multivariate variables is pertinent because predictions from analyzed data are good statistical indicators for making helpful decisions economically and industrially. One of the statistical analytic tools for analyzing multidimensional observations is the kernel density estimator in data exploration and visualization. The functionality of the kernel depends on the kernel function and bandwidth which influences smoothness of estimates. Several kernel functions and bandwidth selectors exist in literature; however novel estimators are being introduced to handle complex circumstances. This paper introduces a new multivariate beta kernel functions whose derivation is contingent on the product techniques. The performances of the newly introduced and existing kernels are evaluated with a known objective function and the numerical results distinctly indicating that the introduced family transcended the traditional beta family