Multivariate Normal Approximation in Geometric Probability
نویسندگان
چکیده
منابع مشابه
Multivariate normal approximation in geometric probability
x ξxδx where the sum is over points x of a Poisson point process of intensity λ on a bounded region in d-space, and ξx is a functional determined by the Poisson points near to x, i.e. satisfying an exponential stabilization condition, along with a moments condition (examples include statistics for proximity graphs, germ-grain models and random sequential deposition models). A known general resu...
متن کاملNormal Approximation in Geometric Probability
Statistics arising in geometric probability can often be expressed as sums of stabilizing functionals, that is functionals which satisfy a local dependence structure. In this note we show that stabilization leads to nearly optimal rates of convergence in the CLT for statistics such as total edge length and total number of edges of graphs in computational geometry and the total number of particl...
متن کاملAdaptive Multivariate Approximation Using Binary Space Partitions and Geometric Wavelets
The Binary Space Partition (BSP) technique is a simple and efficient method to adaptively partition an initial given domain to match the geometry of a given input function. As such the BSP technique has been widely used by practitioners, but up until now no rigorous mathematical justification to it has been offered. Here we attempt to put the technique on sound mathematical foundations, and we ...
متن کاملMultivariate normal approximation using Stein’s method and Malliavin calculus
We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our results generalize and refine the main findings by Peccati and Tudor (2005), Nualart and Ortiz-Latorre (2007), Peccati (2007) and Nourdin and Peccati (2007b, 2008); in particular, they apply to appr...
متن کاملMultivariate approximation
The lecture addresses topics in multivariate approximation which have caught the author’s interest in the last ten years. These include: the approximation by functions with fewer variables, correct points for polynomial interpolation, the B(ernstein,-ézier, -arycentric)-form for polynomials and its use in understanding smooth piecewise polynomial (pp) functions, approximation order from spaces ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Theory and Practice
سال: 2008
ISSN: 1559-8608,1559-8616
DOI: 10.1080/15598608.2008.10411876