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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