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Let W be a random variable with mean zero and variance σ2. The distribution of a variate W ∗, satisfying EWf(W ) = σ2Ef ′(W ∗) for smooth functions f , exists uniquely and defines the zero bias… (More)

Stein’s method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any nonnegative random vector.… (More)

- O Borgan, Bryan Langholz, Sven Ove Samuelsen, Larry Goldstein, Janice M. Pogoda
- Lifetime data analysis
- 2000

A variant of the case-cohort design is proposed for the situation in which a correlate of the exposure (or prognostic factor) of interest is available for all cohort members, and exposure information… (More)

- Larry Goldstein
- 2005

Berry–Esseen-type bounds to the normal, based on zeroand size-bias couplings, are derived using Stein’s method. The zero biasing bounds are illustrated in an application to combinatorial central… (More)

Let Y be a nonnegative random variable with mean μ and finite positive variance σ, and let Y , defined on the same space as Y , have the Y size biased distribution, that is, the distribution… (More)

- Larry Goldstein
- 2007

The zero bias distribution W ∗ of W , defined though the characterizing equation EWf(W ) = σ2Ef ′(W ∗) for all smooth functions f , exists for all W with mean zero and finite variance σ2. For W and W… (More)

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… (More)

- Larry Goldstein
- 2004

Given F : [a, b]k → [a, b] and a non-constant X0 with P (X0 ∈ [a, b]) = 1, define the hierarchical sequence of random variables {Xn}n≥0 by Xn+1 = F (Xn,1, . . . , Xn,k), where Xn,i are i.i.d. as Xn.… (More)

Let $\lambda$ be the second largest eigenvalue in absolute value of a uniform random $d$-regular graph on $n$ vertices. It was famously conjectured by Alon and proved by Friedman that if $d$ is fixed… (More)

Let Y be a nonnegative random variable with mean μ and finite positive variance σ, and let Y , defined on the same space as Y , have the Y size biased distribution, that is, the distribution… (More)