Towards Practical Mean Bounds for Small Samples

06/06/2021
by   My Phan, et al.
0

Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffding's inequality that use weaker assumptions but produce much looser (wider) intervals. In 1969, Anderson (1969) proposed a mean confidence interval strictly better than or equal to Hoeffding's whose only assumption is that the distribution's support is contained in an interval [a,b]. For the first time since then, we present a new family of bounds that compares favorably to Anderson's. We prove that each bound in the family has guaranteed coverage, i.e., it holds with probability at least 1-α for all distributions on an interval [a,b]. Furthermore, one of the bounds is tighter than or equal to Anderson's for all samples. In simulations, we show that for many distributions, the gain over Anderson's bound is substantial.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

05/15/2019

A New Confidence Interval for the Mean of a Bounded Random Variable

We present a new method for constructing a confidence interval for the m...
08/31/2018

Improved Chebyshev inequality: new probability bounds with known supremum of PDF

In this paper, we derive new probability bounds for Chebyshev's inequali...
07/10/2020

Learning Entangled Single-Sample Gaussians in the Subset-of-Signals Model

In the setting of entangled single-sample distributions, the goal is to ...
02/28/2018

Partial Identification of Expectations with Interval Data

A conditional expectation function (CEF) can at best be partially identi...
04/07/2021

The shortest confidence interval for Poisson mean

The existence of the shortest confidence interval for Poisson mean is sh...
03/23/2021

Improving and benchmarking of algorithms for Γ-maximin, Γ-maximax and interval dominance

Γ-maximin, Γ-maximax and inteval dominance are familiar decision criteri...
06/06/2018

Error analysis for small-sample, high-variance data: Cautions for bootstrapping and Bayesian bootstrapping

Recent advances in molecular simulations allow the direct evaluation of ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.