• Corpus ID: 235359146

Towards Practical Mean Bounds for Small Samples

@inproceedings{Phan2021TowardsPM,
  title={Towards Practical Mean Bounds for Small Samples},
  author={My Phan and Philip S. Thomas and Erik G. Learned-Miller},
  booktitle={ICML},
  year={2021}
}
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 (1969a) 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… 
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References

SHOWING 1-10 OF 30 REFERENCES
CONFIDENCE LIMITS FOR THE EXPECTED VALUE OF AN ARBITRARY BOUNDED RANDOM VARIABLE WITH A CONTINUOUS DISTRIBUTION FUNCTION
Abstract : Consider a random variable X with a continuous cumulative distribution function F(x) such that F(a) = 0 and F(b) = 1 for known finite numbers a and b (a < b). The distribution function
Towards practical mean bounds for small
  • 2021
Estimating means of bounded random variables by betting
TLDR
A general approach for deriving concentration bounds that can be seen as a generalization (and improvement) of the celebrated Chernoff method, based on deriving a new class of composite nonnegative martingales, with strong connections to testing by betting and the method of mixtures.
Three test statistics for a nonparametric one-sided hypothesis on the mean of a nonnegative variable
Assume the nonparametric model of n i. i. d. nonnegative real random variables whose distribution is unknown. Consider the one sided hypotheses on the expectation, H0 : μ ≤ 1 vs. H1 : μ > 1. Wang &
A New Confidence Interval for the Mean of a Bounded Random Variable
TLDR
A new method is presented for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable that requires that the distribution be bounded on a known finite interval.
Probability inequalities for sum of bounded random variables
Abstract Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S
Probability Inequalities for the Sum of Independent Random Variables
Abstract This paper proves a number of inequalities which improve on existing upper limits to the probability distribution of the sum of independent random variables. The inequalities presented
Estimating the Total Overstatement Error in Accounting Populations
Abstract Auditors wishing to estimate the total amount of errors in a set of accounts have tended to use estimation procedures which rely on approximate normality for large sample sizes. Since this
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