Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-of-fit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for R\'{e}nyi entropy based on nearest neighbour distances. We prove the L^2-consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods. In addition we present a novel iterative method for estimating the shape parameter of the multivariate Student and multivariate Pearson type II distributions.
翻译:英特罗比及其各种概括性在许多领域都很重要,包括数学统计、通信理论、物理和计算机科学,以说明与概率分布有关的信息数量。在本文中,我们建议根据最大英特罗比原则和R\'{e}nyi entropy的测算器类别,为多异类学生和多异类Pearson II 类分布提供适合的统计。我们用最近的近邻图中Euclidea功能的亚相异性结果,并用蒙特卡洛方法调查其趋同率和无异类分布。此外,我们提出了一种新的迭代方法,用以估计多异类学生和多异类Pearson II 分布的形状参数。