Related papers: Moderate deviations for the $L_1$-norm of kernel d…

Nonparametric kernel density estimation is a very natural procedure which simply makes use of the smoothing power of the convolution operation. Yet, it performs poorly when the density of a positive variable is to be estimated (boundary…

We focus on the nonparametric density estimation problem with directional data. We propose a new rule for bandwidth selection for kernel density estimation. Our procedure is automatic, fully data-driven and adaptive to the smoothness degree…

We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…

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…

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

Given a sample from a discretely observed compound Poisson process, we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. An order bound for…

The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…

We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior…

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclical effects. In particular we extend the results of Ho and Hsing (1996a) and Mielniczuk (1997) to the stationary processes for…

We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…

We show that L^2-bounded singular integral in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost…

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;…

In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al. [2009. The stochastic…

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…

We consider infinite matrices obtained by restricting Hardy integral kernels to natural numbers. For a suitable class of Hardy kernels we describe the absolutely continuous spectrum, the essential spectrum and the asymptotic spectral…

The $L\_2$-minimax risk in Sobolev classes of densities with non-integer smoothness index is shown to have an analog form to that in integer Sobolev classes. To this end, the notion of Sobolev classes is generalized to fractional…

The kernel estimator is known not to be adequate for estimating the density of a positive random variable X. The main reason is the well-known boundary bias problems that it suffers from, but also its poor behaviour in the long right tail…

Let $\theta$ and $\mu$ denote the location and the size of the mode of a probability density. We study the joint convergence rates of semirecursive kernel estimators of $\theta$ and $\mu$. We show how the estimation of the size of the mode…

It seems self-evident that a density functional calculation should be normalized to the number of electrons in the system. We present multiple examples where the accuracy of the approximate energy is improved (sometimes greatly) by…

In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…