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This research aims to derive asymptotic confidence intervals for the mean of a random variable with increased finite-sample coverage probabilities.

December 9, 2025MathematicsOpen Access

Asymptotic Confidence Intervals for the Mean with Increased Finite-Sample Coverage Probabilities

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Asymptotic confidence intervals enhance coverage probabilities for random variables, suggesting advantages over traditional methods.

This research aims to derive asymptotic confidence intervals for the mean of a random variable with increased finite-sample coverage probabilities.
Utilized a Student process based on independent copies of a random variable X.
Derived asymptotic confidence intervals using a functional Central Limit Theorem (FCLT).
Analyzed coverage probabilities for right-skewed distributions in the domain of attraction of the normal law.
Asymptotic confidence intervals exhibit higher finite-sample coverage probabilities compared to traditional confidence intervals based on the Student t-statistic.
For right-skewed distributions, the new confidence intervals may be preferred over existing methods due to improved coverage.

Bhardwaj et al. (2025) studied this question.

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