A Combinatorial Central Limit Theorem

1951/12/01 by Wassily Hoeffding · 2 citations
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.1214/aoms/1177729545

Abstract

Let (Y_n1, ⋯, Y_nn) be a random vector which takes on the n! permutations of (1, ⋯, n) with equal probabilities. Let c_n(i, j), i,j = 1, ⋯, n, be n² real numbers. Sufficient conditions for the asymptotic normality of S_n = ∑ⁿ_i=1 c_n(i, Y_ni) are given (Theorem 3). For the special case c_n(i,j) = a_n(i)b_n(j) a stronger version of a theorem of Wald, Wolfowitz and Noether is obtained (Theorem 4). A condition of Noether is simplified (Theorem 1).

Cited by

• The Analysis of Spatial Association by Use of Distance Statistics
• Conditions of the Central-Limit Theorem Are Rarely Satisfied in Empirical Psychological Studies. [europepmc]

Related

• A central limit theorem for a generalization of the Ewens measure to random tuples of commuting permutations
• Central limit theorem for peaks of a random permutation in a fixed conjugacy class of S_n
• A central limit theorem for a new statistic on permutations
• Central Limit Theorems via Analytic Combinatorics in Several Variables
• Moments of permutation statistics and central limit theorems