Statistical Applications of metric entropy methods

在用数学模型描述时变数据时，检验模型是否与数据拟合的问题称为“优度”问题。适合测试”。这类问题的检验统计量通常没有明确的表达式。然而，当观察时间段较长时，这种测试的分布可以近似为标准布朗运动的泛函。这种情况被称为“渐近分布自由”。本研究项目的主要成果之一是成功地在各种统计模型中构造了这样的检验统计量。

In mathematical models to describe some data which is varying from time to time, the problem to check if the model fits the data or not is called" goodness-of. fit test". Usually, the test statistics for such problems do not have an explicite expression. However, when the observation time period is long, the distribution of such a test can be approximated by a functional of standard Brownian motions. Such a situation is called "asymptotically distribution free". One of the main results in this research project is to have succeeded in constructing such test statistics in various statistical models.