相关论文: Weighted uniform consistency of kernel density est…

We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a…

Consistency of the kernel density estimator requires that the kernel bandwidth tends to zero as the sample size grows. In this paper we investigate the question of whether consistency is possible when the bandwidth is fixed, if we consider…

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

We aim at estimating in a non-parametric way the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$, for $d \ge 2$, from the discrete observations of a finite sample…

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…

In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…

It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for…

We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…

We construct near-optimal coresets for kernel density estimates for points in $\mathbb{R}^d$ when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size $O(\sqrt{d}/\varepsilon\cdot…

Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…

Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma_n Z_i$ and the $Y$'s and $Z$'s are independent. Assume that the $Y$'s are unobservable and that they have the density $f$ and also that the $Z$'s have a known density $k.$…

The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…

The rate of normal approximation for the integral norm of kernel density estimators is investigated in the case of densities with power-type singularities. The quantities from the formulations of published results by the author are…

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…

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…

We consider real sequences $(f_n)$ that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case where the sequence has no positive…

Let $f$ be a multivariate density and $f\_n$ be a kernel estimate of $f$ drawn from the $n$-sample $X\_1,...,X\_n$ of i.i.d. random variables with density $f$. We compute the asymptotic rate of convergence towards 0 of the volume of the…

We study non-stationary averaging processes, where each term of a sequence is a weighted average of previous terms, namely $a_{n+1} = \sum_{j=1}^n p_n(j) a_j$. Our results extend classical theory in two distinct regimes. First, we prove a…

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…