On a Probabilistic Algorithm for Solving Some Problems in Robust Statistics

On A Probabilistic Algorithm For Solving Some Problems in Robust Statistics
Biman Chakraborty

In this talk, we consider a large class of computational problems in robust statistics which can be formulated as selection of optimal subsets of data based on some criterion function. To solve such problems, we discuss that there are largely two classes of algorithms available in the literature, one is based on completely random search and the other is based on deterministically guided strategies. Though these methods can achieve satisfactory results in some specific examples, none of them can be used satisfactorily for a large class of similar problems either due their very long expected waiting time to hit the true optimum or due to their failure to come out of a local optima when they get trapped in one. Here, we propose two probabilistic search algorithms, which proceed through some iterative schemes. Under some conditions on the parameters of the algorithms, we establish the convergence of our algorithms to the true optimum. We also present some results on probability of hitting the true optimum if the algorithms are run for a finite number of iterations. Finally, we compare the performance of our algorithms to some commonly available algorithms to compute some popular robust and multivariate statistics using real data sets.

Lisätietoja: assistentti Kimmo Ivori, etunimi.sukunimi@uta.fi