Statistical Applications of metric entropy methods

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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.