Multinomial Goodness-of-Fit Based on U-Statistics: High-Dimensional Asymptotic and Minimax Optimality

12/21/2018
by   Ilmun Kim, et al.
0

We consider multinomial goodness-of-fit tests in the high-dimensional regime where the number of bins increases with the sample size. In this regime, Pearson's chi-squared test can suffer from low power due to the substantial bias as well as high variance of its statistic. To resolve these issues, we introduce a family of U-statistic for multinomial goodness-of-fit and study their asymptotic behaviors in high-dimensions. Specifically, we establish conditions under which the considered U-statistic is asymptotically Poisson or Gaussian, and investigate its power function under each asymptotic regime. Furthermore, we introduce a class of weights for the U-statistic that results in minimax rate optimal tests.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset