Boundary Crossing Probabilities for U-Statistics.

Abstract

Let the set (U sub n, n > or = r) be a sequence of U-statistics with mean theta. The author computes upper bounds on the probabilities P(U sub n - theta > or = a sub n for some n > or = m) and P(/U sub n - theta / > or = a sub n for some n > or = m) for certain for certain boundary sequences including a sub n = O(square root (2 loglog n/n)). An invariance theorem is also deduced. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 17, 1971
Accession Number
AD0743789

Entities

People

  • Rasul A. Khan

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Crossings
  • Data Science
  • Information Science
  • Invariance
  • Mathematics
  • Probability
  • Sequences
  • Square Roots
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.