9803344 Mason Large sample problems in probability and statistics concern what happens to processes or statistics when the sample size increases to infinity. The investigator plans to work in three areas in which such problems naturally arise. These are the following: 1. self-normalized sums, 2. generalized extremes, and 3. weighted approximations. The problems in area 1 originate from the long standing question concerning the possible asymptotic distributions of the classical Student's t-statistic. Those in area 2 stem from questions about the limiting distribution of extreme values, such as annual maximum temperatures, river heights and largest incomes in a population. He generalizes the notion of extremes to a multivariate setting and proposes to study its large sample properties. Finally in area 3, he intends to look into methods of approximating finite sample processes that arise from testing for dependence in data by an asymptotic process. This should provide a useful tool to determine the limiting distribution of many functionals of such finite sample processes. Solutions to problems in all three areas of research should have numerous applications in statistical inference and estimation, especially in multivariate and dependent situations, whenever large samples are available. Eventually, it is hoped that many of the results will lead to the construction of data analytic tools which will enter into the everyday practice of statistics. In any case they should improve our understanding of an interesting range of random behavior.
