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...

We give error bounds which demonstrate optimal rates of convergence in the CLT for the total covered volume and the number of isolated shapes, for germ-grain models with fixed grain radius over a binomial point process of n points in a toroidal spatial region of volume n. The proof is based on Stein's method via size-biased couplings. 1. Introduction. Given a collection of n independent uniform...

In a convolution model, we observe random variables whose distribution is the convolution of some unknown density f and some known noise density g. We assume that g is polynomially smooth. We provide goodness-of-fit testing procedures for the test H0 : f = f0, where the alternative H1 is expressed with respect to L2-norm (i.e. has the form ψ−2 n ‖f −f0‖2 ≥ C). Our procedure is adaptive with res...