论文标题
限制定理的无限性urn中非空urn数量的前向和向后过程
Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes
论文作者
论文摘要
我们研究了无限的urn方案中非空urn数量的前向和后退过程的联合渐近学。假定击中球的球的概率可以满足定期减少的条件。我们证明了弱收敛到二维高斯过程。它的协方差函数仅取决于定期下降概率的指数。我们获得具有正常分布的正常分布的参数估计值，以及前向和向后过程。我们使用这些估计值来构建针对投掷球数的urn方案均匀性的统计测试。
We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak convergence to a two-dimensional Gaussian process. Its covariance function depends only on exponent of regular decrease of probabilities. We obtain parameter estimates that have a normal asymototics for its joint distribution together with forward and backward processes. We use these estimates to construct statistical tests for the homogeneity of the urn scheme on the number of thrown balls.
