Hi all,
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.
