Corpus ID: 305655

# An unbiased estimate for the mean of a {0, 1} random variable with relative error distribution independent of the mean

@article{Huber2013AnUE,
title={An unbiased estimate for the mean of a \{0, 1\} random variable with relative error distribution independent of the mean},
author={Mark Huber},
journal={ArXiv},
year={2013},
volume={abs/1309.5413}
}
• Mark Huber
• Published 2013
• Computer Science, Mathematics
• ArXiv
• Say $X_1,X_2,\ldots$ are independent identically distributed Bernoulli random variables with mean $p$. This paper builds a new estimate $\hat p$ of $p$ that has the property that the relative error, $\hat p /p - 1$, of the estimate does not depend in any way on the value of $p$. This allows the construction of exact confidence intervals for $p$ of any desired level without needing any sort of limit or approximation. In addition, $\hat p$ is unbiased. For $\epsilon$ and $\delta$ in $(0,1)$, to… CONTINUE READING

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