Published February 2022 | Accepted Version
Journal Article Open

On the Le Cam Distance Between Multivariate Hypergeometric and Multivariate Normal Experiments

An error occurred while generating the citation.

Abstract

In this short note, we develop a local approximation for the log-ratio of the multivariate hypergeometric probability mass function over the corresponding multinomial probability mass function. In conjunction with the bounds from Carter (Ann Stat 30(3):708–730, 2002) and Ouimet (J Stat Plan Inference 215:218–233, 2021) on the total variation between the law of a multinomial vector jittered by a uniform on (−1/2,1/2)^d and the law of the corresponding multivariate normal distribution, the local expansion for the log-ratio is then used to obtain a total variation bound between the law of a multivariate hypergeometric random vector jittered by a uniform on (−1/2,1/2)^d and the law of the corresponding multivariate normal distribution. As a corollary, we find an upper bound on the Le Cam distance between multivariate hypergeometric and multivariate normal experiments.

Additional Information

© 2021 The Author(s), under exclusive licence to Springer Nature Switzerland AG. Received 24 July 2021; Accepted 29 November 2021; Published 03 January 2022. The author thanks the referee for his/her comments. The author is supported by postdoctoral fellowships from the NSERC (PDF) and the FRQNT (B3X supplement and B3XR).

Attached Files

Accepted Version - 2107.11565.pdf

Files

2107.11565.pdf
Files (128.9 kB)
Name Size Download all
md5:eb65fcd5b7fc510600ff3694d4fe5ab5
128.9 kB Preview Download

Additional details

Created:
August 22, 2023
Modified:
October 23, 2023