Alon Kipnis- The minimax risk in testing uniformity under missing ball alternatives
סמינר מחלקת מערכות - EE Systems Seminar
Electrical Engineering Systems Seminar
(The talk will be given in English)
Speaker: Alon Kipnis - School of Computer Science, Reichman University
011 hall, Electrical Engineering-Kitot Building
Monday, May 27th, 2024
12:00-13:00
The minimax risk in testing uniformity under missing ball alternatives
Abstract
We study the problem of testing the goodness of fit of a sample to a uniform distribution over many categories. We consider a minimax setting in which the class of alternatives is obtained by the removal of an Lp ball of radius r around the uniform rate sequence. We provide an expression describing the asymptotic minimax risk in terms of r, p, the number of categories, and the size of the sample.
Our result settles an open question related to works on identity testing in computer science and nonparametric hypothesis testing on distributions in mathematical statistics. It allows the comparison of the many estimators previously proposed for this problem at the constant level, rather than at the rate of convergence of the risk or the scaling order of the sample complexity.
The minimax test mostly relies on collisions in the very small sample limit but behaves like the chi-squared test for moderate and large sample sizes. Empirical studies over a range of problem parameters show that our asymptotic estimate of the minimax risk is accurate in finite samples and that the asymptotic minimax test is significantly better than the chi-squared test or a test that only uses collisions.
Short Bio
Alon Kipnis is a senior lecturer at the School of Computer Science at Reichman University. He received the Ph.D. in electrical engineering from Stanford University in 2017. Between 2017-2021 he was a postdoctoral research scholar and a lecturer at the Department of Statistics at Stanford, advised by David Donoho. Dr. Kipnis' research combines mathematical statistics, information theory, signal processing, and ambitious data science.
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