2007/09/01 by Larry Goldstein · 24 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Constant (computer programming) #Cumulative distribution function #Distribution (mathematics) #Limit (mathematics) #Mathematical Approximation and Integration #Measure (data warehouse) #Probability distribution #Random Matrices and Applications #Random variable #Simple (philosophy) #Upper and lower bounds #Zero (linguistics) #math.PR #msc:60C05 #msc:60D05 #msc:60F05 #msc:60F25
paper · pdf · doi:10.1214/009117906000001123
published in The Annals of Probability 35(5) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/009117906000001123 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2007/09/01 · arxiv created 2007/10/17 · arxiv updated 2011/11/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The zero bias distribution W* of W, defined though the characterizing equation EW f(W)=σ2E f'(W*) for all smooth functions f, exists for all W with mean zero and finite variance σ2. For W and W* defined on the same probability space, the L1 distance between F, the distribution function of W with EW=0 and Var(W)=1, and the cumulative standard normal Φ has the simple upper bound ‖F−Φ‖1≤2E|W*−W|. This inequality is used to provide explicit L1 bounds with moderate-sized constants for independent sums, projections of cone measure on the sphere S(ℓnp), simple random sampling and combinatorial central limit theorems.