Our first Information Theory and Applications seminar for the academic year will take place on Monday, November 4 at 10:00, in room A500.

The speaker this week is Royi Jacobovic, who will tell us about new results on Moran's single-split test. See title and abstract below.

See you there,

Or, Oron, Yuval and Alex

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Title: Simple sufficient condition for inadmissibility of Moran's single-split test.

Abstract: Suppose that a statistician has two iid observations that each of them is equal to the parameter of the model plus a random noise. His purpose is to test whether the 

parameter is zero with a pre-defined significance level. Moran (1973) suggested a test which is based on a single split of the data, i.e., to use the second observation in order to conduct a one-sided test in the direction of the first observation.  Moran mentioned that when the noise is distributed according to a normal distribution, the power of this test is
not greater than the power of the standard two-sided Z-test. In this work, we generalize this result by providing a condition on the distribution of the noise under which
Moran's test is inadmissible. The proof of these results follows from an analysis of a new notion, regular admissibility of tests. Furthermore, when the parameter (and the observations) are vectors, the current analysis yields a new characterization of the multivariate normal distribution via convex likelihood ratios.

The seminar is based on two works:

Jacobovic, R. (2022). Simple sufficient condition for inadmissibility of Moran’s single-split test. Electronic Journal of Statistics, 16, 3036-3059.

Jacobovic, R., & Kella, O. (2022). A characterization of normality via convex likelihood ratios. Statistics & Probability Letters , 186 , 109455.