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Does anyone have any reference for a sequential estimator for proportions?

I am planning an experiment to measure the probability of a certain event happening and would like to know how many observations to take to estimate it to within a certain accuracy. Clearly, this will depend of the size of the probability we end up observing about which our option will change sequentially as we obtain more information.

Classical Wald sequential ratio tests can be very efficient for two groups. Is there a parallel for the one sample case.

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Wald's SPRT (sequential probability ratio test) was not originally formulated as a two group comparison test:

https://en.wikipedia.org/wiki/Sequential_probability_ratio_test

The "bible" for sequential analysis is probably last year's book Sequential Analysis: Hypothesis Testing and Changepoint Detection by Alexander Tartakovsky. It is magisterial and seemingly exhaustive in its coverage of the topic.

http://www.amazon.com/Sequential-Analysis-Hypothesis-Changepoint-Probability-ebook/dp/B00MMOIWTS/ref=sr_1_1?ie=UTF8&qid=1445511005&sr=8-1&keywords=sequential+analysis+tartakovsky

That said, last June Columbia sponsored The Fifth International Workshop in Sequential Methodologies which brought together the latest and greatest practitioners in the field. Tartakovsky was on the organizing committee.

https://sites.google.com/site/iwsm2015/home

See the "Detailed Program" link on the conference website for abstracts and papers. There's probably something there targeted specifically to your question.

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  • $\begingroup$ you're right. Its the hypothesis testing aspect that sets the SPRT apart from my estimation problem. Will follow up the links and then mark it as solved when I find a reference. Many thanks. $\endgroup$ – drw Oct 22 '15 at 11:05

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