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AMS Seminar: Jim Fill (JHU- AMS) @ Whitehead 304
October 3, 2019 @ 1:30 pm - 2:30 pm
Title: Multivariate Pareto Records
Abstract: Consider i.i.d. d-dimensional observations with independent coordinates, each with (say) the standard Exponential distribution. Say that the n-th observation sets a (Pareto) record if it is not dominated by any of the first n – 1 observations. If k is in {1, …, n}, say that the k-th observation is a current record at time n if it sets a record and is not dominated by any of the next n – k observations; and say that the n-th observation breaks the record set by the k-th observation if the k-th observation is a current record at time n – 1 but not at time n.
We will discuss one or more of the following topics: (i) an efficient algorithm for the simulation of Pareto records, and its (partial) analysis; (ii) the location and thickness of the record frontier; (iii) how the Geometric(1/2) distribution arises in connection with the breaking of bivariate records.
This is joint work with Daniel Q. Naiman.