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Distributed inference for degenerate U ‐statistics
Author(s) -
AttaAsiamah Ernest,
Yuan Mingao
Publication year - 2019
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.234
Subject(s) - statistics , disjoint sets , divide and conquer algorithms , degenerate energy levels , partition (number theory) , computation , inference , statistical hypothesis testing , statistical inference , order statistic , mathematics , computer science , algorithm , discrete mathematics , combinatorics , artificial intelligence , physics , quantum mechanics
In many hypothesis testing problems, the test statistics are degenerate U ‐statistics. One of the challenges in practice is the computation of U ‐statistics for large dataset. In this paper, we aim to reduce the computation complexity of degenerate U ‐statistics by using the divide‐and‐conquer method. Specifically, we partition the full n data points into k n even disjoint groups, compute the U ‐statistics on each group, and combine them by averaging. In this way, the running time is reduced to O (n mk n m − 1) , where m is the order of the U ‐statistics. Besides, we study the optimal test rate of the divide‐and‐conquer methods. For degenerate U ‐statistics, the optimal rate is n , the same as the optimal test rate for the nondegenerate case. The simulation and real data confirm that the proposed method has high power and faster running time.