Related papers: Kernel density estimation with polyspherical data …

In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…

The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some…

We study theoretically, for the first time, the Dirichlet kernel estimator introduced by Aitchison and Lauder (1985) for the estimation of multivariate densities supported on the $d$-dimensional simplex. The simplex is an important case as…

Nonparametric estimation of copula density functions using kernel estimators presents significant challenges. One issue is the potential unboundedness of certain copula density functions at the corners of the unit square. Another is the…

We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric…

We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum…

Nonparametric density estimation for compositional data supported on the simplex is examined under a missing at random mechanism. Rather than imputing missing values and estimating the density from a completed data set, we adopt a strategy…

We propose nonparametric estimation of divergence measures between continuous distributions. Our approach is based on a plug-in kernel- type estimators of density functions. We give the uniform in bandwidth consistency for the proposal…

It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation,…

We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…

There is an intense and partly recent literature focussing on the problem of selecting the bandwidth parameter for kernel density estimators. Available methods are largely `very nonparametric', in the sense of not requiring any knowledge…

In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous…

Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…

Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…

It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), Improved Variable Window Kernel Estimates of Probability Densities, {\it Annals of Statistics}, 23, 1--10] modification of Abramson's [Abramson, I. (1982),…

Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…

Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…

This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…

In this work, we establish the asymptotic normality of the deconvolution kernel density estimator in the context of strongly mixing random fields. Only minimal conditions on the bandwidth parameter are required and a simple criterion on the…

The kernel smoothing with large bandwidth values causes oversmoothing or underfitting in general. However, when irrelevant variables are included, the corresponding large bandwidth values are known to have an effect of shrinking them. This…