The least favorable noise
File(s)
Published version
Author(s)
Ernst, Philip A
Kagan, Abram M
Rogers, LCG
Type
Journal Article
Abstract
Suppose that a random variable X of interest is observed perturbed by independent additive noise Y. This paper concerns the “the least favorable perturbation”
ˆ
Y
ε
, which maximizes the prediction error
E
(
X
−
E
(
X
|
X
+
Y
)
)
2
in the class of Y with
v
a
r
(
Y
)
≤
ε
. We find a characterization of the answer to this question, and show by example that it can be surprisingly complicated. However, in the special case where X is infinitely divisible, the solution is complete and simple. We also explore the conjecture that noisier Y makes prediction worse.
ˆ
Y
ε
, which maximizes the prediction error
E
(
X
−
E
(
X
|
X
+
Y
)
)
2
in the class of Y with
v
a
r
(
Y
)
≤
ε
. We find a characterization of the answer to this question, and show by example that it can be surprisingly complicated. However, in the special case where X is infinitely divisible, the solution is complete and simple. We also explore the conjecture that noisier Y makes prediction worse.
Date Issued
2022-05-17
Date Acceptance
2022-04-16
Citation
Electronic Communications in Probability, 2022, 27 (none), pp.1-11
ISSN
1083-589X
Publisher
Institute of Mathematical Statistics
Start Page
1
End Page
11
Journal / Book Title
Electronic Communications in Probability
Volume
27
Issue
none
Copyright Statement
© The Author(s) 2022. This work is published under CC BY 4.0 International licence.
License URL
Identifier
https://projecteuclid.org/journals/electronic-communications-in-probability/volume-27/issue-none/The-least-favorable-noise/10.1214/22-ECP467.full
Subjects
Statistics & Probability
0104 Statistics
Publication Status
Published
Date Publish Online
2022-05-17