TITLE: Convergence rates for MLE estimators and dynamic pricing applications

SPEAKER: Dr. Bert Zwart

ABSTRACT:

We consider a generalized linear model where data may be collected in an adapted fashion. Even in the linear case, consistency of MLE/regression estimators is a nontrivial problem, and sufficient conditions are typically given in terms of eigenvalues of the design matrix. This setting has been studied extensively by economists, statisticians and control theorists, but has gained renewed interest given the recent activities on dynamic pricing under demand uncertainty. In terms of dynamic pricing, it can be shown that the so-called 'certainty equivalent pricing' policy does not lead to consistent results, and price dispersion is necessary. We establish general L2 convergence rates for MLE estimators in terms of eigenvalues of the design matrix and apply these on dynamic pricing problems. We develop algorithms that are computationally tractable and give guaranteed bounds on the regret (the loss in profit related to parameter uncertainty).

Joint work with Arnoud den Boer (CWI)