Asymptotic mean values of Gaussian polytopes
نویسندگان
چکیده
We consider geometric functionals of the convex hull of normally distributed random points in Euclidean space R. In particular, we determine the asymptotic behaviour of the expected value of such functionals and of related geometric probabilities, as the number of points increases.
منابع مشابه
Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data
The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for ...
متن کاملOptimum Block Size in Separate Block Bootstrap to Estimate the Variance of Sample Mean for Lattice Data
The statistical analysis of spatial data is usually done under Gaussian assumption for the underlying random field model. When this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. One of the crucial problems in this setting is specifying the block sizes. In this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the...
متن کاملAsymptotic Euler-Maclaurin formula for Delzant polytopes
Formulas for the Riemann sums over lattice polytopes determined by the lattice points in the polytopes are often called Euler-Maclaurin formulas. An asymptotic Euler-Maclaurin formula, by which we mean an asymptotic expansion formula for Riemann sums over lattice polytopes, was first obtained by Guillemin-Sternberg [GS]. Then, the problem is to find a concrete formula for the each term of the e...
متن کاملAsymptotic estimates for best and stepwise approximation of convex bodies III
We consider approximations of a smooth convex body by inscribed and circumscribed convex polytopes as the number of vertices, resp. facets tends to innnity. The measure of deviation used is the diierence of the mean width of the convex body and the approximating polytopes. The following results are obtained. (i) An asymptotic formula for best approximation. (ii) Upper and lower estimates for st...
متن کاملAsymptotic approximation of smooth convex bodies by general polytopes
For the optimal approximation of convex bodies by inscribed or circumscribed polytopes there are precise asymptotic results with respect to different notions of distance. In this paper we want to derive some results on optimal approximation without restricting the polytopes to be inscribed or circumscribed. Let Pn and P(n) denote the set of polytopes with at most n vertices and n facets, respec...
متن کامل