Optimal testing of statistical hypotheses and multiple familywise error rates

Sequential Tests of Multiple Hypotheses Controlling Type I and II Familywise Error Rates.

This paper addresses the following general scenario: A scientist wishes to perform a battery of experiments, each generating a sequential stream of data, to investigate some phenomenon. The scientist would like to control the overall error rate in order to draw statistically-valid conclusions from each experiment, while being as efficient as possible. The between-stream data may differ in distr...

A Rejection Principle for Sequential Tests of Multiple Hypotheses Controlling Familywise Error Rates.

We present a unifying approach to multiple testing procedures for sequential (or streaming) data by giving sufficient conditions for a sequential multiple testing procedure to control the familywise error rate (FWER). Together we call these conditions a "rejection principle for sequential tests," which we then apply to some existing sequential multiple testing procedures to give simplified unde...

Statistical Testing of Hypotheses

Multiple Objects: Error Exponents in Hypotheses Testing and Identification

“One can conceive of Information Theory in the broad sence as covering the theory of Gaining, Transferring, and Storing Information, where the first is usually called Statistics.”[2]. Shannon information theory and mathematical statistics interaction revealed to be effective. This interplay is mutually fruitful, in some works results of probability theory and statistics were obtained with appli...

Optimal Rates and Tradeoffs in Multiple Testing

Multiple hypothesis testing is a central topic in statistics, but despite abundant work on the false discovery rate (FDR) and the corresponding Type-II error concept known as the false non-discovery rate (FNR), a fine-grained understanding of the fundamental limits of multiple testing has not been developed. Our main contribution is to derive a precise non-asymptotic tradeoff between FNR and FD...