Estimating a Distribution Function When New is Better Than Used.
Interim technical rept.,
CALIFORNIA UNIV DAVIS INTERCOLLEGE DIV OF STATISTICS
Pagination or Media Count:
The problem we study in this paper is the estimation of the distribution function F under the assumption that F belongs to the class of NBU distributions. Without the NBU restriction, the empirical distribution function Fn converges to F in several senses and at the best possible rate. However, Fn need not to be NBU, and, in fact, it is not difficult to show that Pfn is NBU going to 0 when sampling from some NBU distributions for example, the exponential distribution. Our goal here is to construct a sequence Fn of NBU distributions which achieve the same asymptotic optimality as the sequence Fn.
- Statistics and Probability