Stein’s method via induction
Copyright policy )Stein’s method via induction
Applying an inductive technique for Stein and zero bias couplings yields Berry-Esseen theorems for normal approximation for two new examples. The conditions of the main results do not require that the couplings be bounded. Our two applications, one to the Erdős-Rényi, random graph with a fixed number of edges, and one to Jack measure on tableaux, demonstrate that the method can handle non-bounded variables with non-trivial global dependence, and can produce bounds in the Kolmogorov metric with the optimal rate.
59 pages
- University of California System United States
- National University of Singapore Libraries Singapore
- National University of Singapore Singapore
optimal rates, Erdős-Rényi random graph, Combinatorial probability, Erd?s-Rényi random graph, 05C80, Probability (math.PR), 60F05 (Primary), 05C07, 05C80, 05E10 (secondary), Optimal rates, Random graphs (graph-theoretic aspects), Stein’s method, Central limit and other weak theorems, Jack measure, 60F05, Combinatorial aspects of representation theory, 05C07, FOS: Mathematics, Mathematics - Combinatorics, Stein's method, Combinatorics (math.CO), Kolmogorov distance, 05E10, Mathematics - Probability
optimal rates, Erdős-Rényi random graph, Combinatorial probability, Erd?s-Rényi random graph, 05C80, Probability (math.PR), 60F05 (Primary), 05C07, 05C80, 05E10 (secondary), Optimal rates, Random graphs (graph-theoretic aspects), Stein’s method, Central limit and other weak theorems, Jack measure, 60F05, Combinatorial aspects of representation theory, 05C07, FOS: Mathematics, Mathematics - Combinatorics, Stein's method, Combinatorics (math.CO), Kolmogorov distance, 05E10, Mathematics - Probability
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