Related papers: A note on kernel density estimators with optimal b…
In this paper, we investigate the supremum-norm generalization error and the uniform inference for a specific class of kernel regression methods, namely the kernel gradient flows. Under the widely adopted capacity-source condition framework…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on…
In this paper several related estimation problems are addressed from a Bayesian point of view and optimal estimators are obtained for each of them when some natural loss functions are considered. Namely, we are interested in estimating a…
This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent advances regarding confidence bands and geometric/topological features. We begin with a discussion of basic properties of KDE: the convergence rate…
Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…
In the current paper, the estimation of the probability density function and the cumulative distribution function of the Topp-Leone distribution is considered. We derive the following estimators: maximum likelihood estimator, uniformly…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…
In this paper we propose an automatic bandwidth selection of the recursive kernel density estimators with missing data in the context of global and local density estimation. We showed that, using the selected bandwidth and a special…
Let $(X_1,\ldots,X_n)$ be an i.i.d. sequence of random variables in $\mathbb{R}^d$, $d\geq 1$. We show that, for any function $\varphi :\mathbb{R}^d\rightarrow\mathbb{R}$, under regularity conditions, \[n^…
The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the…
This paper deals with the kernel density estimator based on the so-called sinc (or Fourier integral) kernel $K(x)=(\pi x)^{-1}\sin x$. We study in detail both asymptotic and finite sample properties of this estimator. It is shown that,…
The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter…
The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack…
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),…
Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the…
In some applications it is necessary to estimate derivatives of probability densities defined on the positive semi-axis. The quality of nonparametric estimates of the probability densities and their derivatives are strongly influenced by…
We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative.…