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We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we…

Statistics Theory · Mathematics 2010-11-12 Z. I. Botev , J. F. Grotowski , D. P. Kroese

This paper studies the minimax rate of nonparametric conditional density estimation under a weighted absolute value loss function in a multivariate setting. We first demonstrate that conditional density estimation is impossible if one only…

Statistics Theory · Mathematics 2021-03-15 Michael Li , Matey Neykov , Sivaraman Balakrishnan

We study the problem of the non-parametric estimation for the density of the stationary distribution of the multivariate stochastic differential equation with jumps (Xt) , when the dimension d is bigger than 3. From the continuous…

Statistics Theory · Mathematics 2021-09-15 Chiara Amorino

In this paper, we deal with the data-driven selection of multidimensional and possibly anisotropic bandwidths in the general framework of kernel empirical risk minimization. We propose a universal selection rule, which leads to optimal…

Statistics Theory · Mathematics 2016-08-11 Michaël Chichignoud , Sébastien Loustau

Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…

Statistics Theory · Mathematics 2018-05-07 Ilja Klebanov

We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of possibly unknown dimension $d < D$ under a reach condition. We study nonparametric kernel…

Statistics Theory · Mathematics 2020-11-02 Clément Berenfeld , Marc Hoffmann

Considering two independent Poisson processes, we address the question of testing equality of their respective intensities. We first propose single tests whose test statistics are U-statistics based on general kernel functions. The…

Statistics Theory · Mathematics 2012-11-15 Magalie Fromont , Béatrice Laurent , Patricia Reynaud-Bouret

The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed…

Statistics Theory · Mathematics 2008-01-22 Patricia Reynaud-Bouret , Vincent Rivoirard

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…

Computation · Statistics 2020-07-21 Anne van Delft , Michael Eichler

We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole…

Statistics Theory · Mathematics 2020-06-22 Christophe Gaillac , Eric Gautier

The paper deals with the problem of nonparametric estimating the $L_p$--norm, $p\in (1,\infty)$, of a probability density on $R^d$, $d\geq 1$ from independent observations. The unknown density %to be estimated is assumed to belong to a ball…

Statistics Theory · Mathematics 2020-08-26 Alexander Goldenshluger , Oleg Lepski

We study a non-parametric approach to multivariate density estimation. The estimators are piecewise constant density functions supported by binary partitions. The partition of the sample space is learned by maximizing the likelihood of the…

Statistics Theory · Mathematics 2015-08-21 Linxi Liu , Wing Hung Wong

We study the problem of the nonparametric estimation for the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$. From the continuous observation of the sampling path on…

Statistics Theory · Mathematics 2023-10-23 Chiara Amorino , Arnaud Gloter

This paper considers the problem of adaptive estimation of a non-homogeneous intensity function from the observation of n independent Poisson processes having a common intensity that is randomly shifted for each observed trajectory. We show…

Statistics Theory · Mathematics 2011-05-20 Jérémie Bigot , Sébastien Gadat , Thierry Klein , Clément Marteau

We consider the problem of statistical learning for the intensity of a counting process with covariates. In this context, we introduce an empirical risk, and prove risk bounds for the corresponding empirical risk minimizers. Then, we give…

Statistics Theory · Mathematics 2009-09-30 Stéphane Gaïffas , Agathe Guilloux

In this paper, we study first the problem of nonparametric estimation of the stationary density $f$ of a discrete-time Markov chain $(X_i)$. We consider a collection of projection estimators on finite dimensional linear spaces. We select an…

Statistics Theory · Mathematics 2008-01-09 Claire Lacour

This paper deals with the problem of the multivariate copula density estimation. Using wavelet methods we provide two shrinkage procedures based on thresholding rules for which the knowledge of the regularity of the copula density to be…

Statistics Theory · Mathematics 2011-11-04 Florent Autin , Erwan Le Pennec , Karine Tribouley

Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…

Statistics Theory · Mathematics 2012-06-14 Judson B. Locke , Adrian M. Peter

This paper deals with estimation with functional covariates. More precisely, we aim at estimating the regression function $m$ of a continuous outcome $Y$ against a standard Wiener coprocess $W$. Following Cadre and Truquet (2015) and Cadre,…

Statistics Theory · Mathematics 2020-11-23 Karine Bertin , Nicolas Klutchnikoff

In this work, we propose new matrix- and tensor-based methodologies for estimating multivariate intensity functions of inhomogeneous point processes. By viewing multivariate intensity functions as infinite-dimensional matrices or tensors…