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Business Analytics

The Cross Moment Model of Choice

Vinit Mishra, Discipline of Business Analytics, University of Sydney Business School

28th Sep 2012  11:00 am - Room 498 Merewether Building H04

Several generalizations of Chebyshev-type (1874) inequalities were published in 1950s and 1960s that proposed tight upper or lower bounds on the expectation of functions of random variables given moments information. When mean-covariance information is given, a tight upper bound on the expectation of highest order statistic can be found using a semidefinite program. Empowered with this result and an extreme point argument, I will propose a method of finding choice probabilities in discrete choice.  This new method, known as Cross Moment Model (CMM), generates choice probabilities using a convex semidefinite program and avoids the evaluation of multidimensional integrals as is typically done in choice models such as multinomial probit. Several simple examples will illustrate power of the proposed approach and beauty of this deterministic way of solving problems with random parameters.