ﻻ يوجد ملخص باللغة العربية
In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it implies positive association. Since estimating a totally positive density is a non-parametric problem, we take on a (modified) kernel density estimation approach. Our main result is that the sum of scaled standard Gaussian bumps centered at a min-max closed set provably yields a totally positive distribution. Hence, our strategy for producing a totally positive estimator is to form the min-max closure of the set of samples, and output a sum of Gaussian bumps centered at the points in this set. We can frame this sum as a convolution between the uniform distribution on a min-max closed set and a scaled standard Gaussian. We further conjecture that convolving any totally positive density with a standard Gaussian remains totally positive.
We study minimax estimation of two-dimensional totally positive distributions. Such distributions pertain to pairs of strongly positively dependent random variables and appear frequently in statistics and probability. In particular, for distributions
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 propose a new p
The purpose of this note is to provide an approximation for the generalized bootstrapped empirical process achieving the rate in Kolmos et al. (1975). The proof is based on much the same arguments as in Horvath et al. (2000). As a consequence, we est
Elliptically contoured distributions generalize the multivariate normal distributions in such a way that the density generators need not be exponential. However, as the name suggests, elliptically contoured distributions remain to be restricted in th
This paper studies the estimation of the conditional density f (x, $times$) of Y i given X i = x, from the observation of an i.i.d. sample (X i , Y i) $in$ R d , i = 1,. .. , n. We assume that f depends only on r unknown components with typically r d