This article is available for purchase or by subscription. See below.
Abstract
|
We study the problem of estimating 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. We take a (modified) kernel density estimation approach to estimate a
totally positive density. Our main result is that the sum of scaled standard Gaussians
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 Gaussians 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.
|
PDF Access Denied
We have not been able to recognize your IP address
18.219.189.247
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
total positivity, kernel density estimation, MTP$_2$
|
Mathematical Subject Classification
Primary: 62G05, 62G07, 62R01
Secondary: 62H20
|
Milestones
Received: 26 December 2020
Revised: 17 January 2022
Accepted: 24 January 2022
Published: 4 May 2023
|
© 2022 MSP (Mathematical Sciences
Publishers). |
|