For a coordinate symmetric random vector (Y1, . . . ,Yn) = Y ∈ R, that is, one satisfying (Y1, . . . ,Yn) =d (e1Y1, . . . , enYn) for all (e1, . . . , en) ∈ {−1,1}, for which P(Yi = 0) = 0 for all i = 1,2, . . . ,n, the following Berry Esseen bound to the cumulative standard normal Φ for the standardized projection Wθ = Yθ/vθ of Y holds: sup x∈R |P(Wθ ≤ x)−Φ(x)| ≤ 2 n ∑ i=1 |θi |E|X i | + 8.4E(...

A Chernoff-type distribution is a nonnormal defined by the slope at zero of greatest convex minorant two-sided Brownian motion with polynomial drift. While known to appear as distributional limit in many nonregular statistical estimation problems, accuracy approximations has remained largely unknown. In present paper, we tackle this problem and derive Berry–Esseen bounds for distributions canon...

The inductive size bias coupling technique and Stein’s method yield a Berry-Esseen theorem for the number of urns having occupancy d ≥ 2 when n balls are uniformly distributed over m urns. In particular, there exists a constant C depending only on d such that sup z∈R |P (Wn,m ≤ z)− P (Z ≤ z)| ≤ C σn,m 1 + ( n m )3 for all n ≥ d and m ≥ 2, where Wn,m and σ 2 n,m are the standardized count and va...

Abstract In this work the $\ell_q$ -norms of points chosen uniformly at random in a centered regular simplex high dimensions are studied. Berry–Esseen bounds regime $1\leq q < \infty$ derived and complemented by non-central limit theorem together with moderate large deviations case where $q=\infty$ . An application to intersection volume an $\ell_p^n$ -ball is also carried out.

This paper develops techniques to study the asymptotic distribution of number descents in random permutations. We relax an assumption Berry-Esseen theorem Bolthausen (1982) extend theorem's scope martingale differences time-dependent variances. present its applications other combinatorial statistics as they satisfy certain recurrence relation conditions. These include inversions, signed permuta...