Congratulations are extended to Professor Lars Stentoft, whose Tier II CRC in Financial Econometrics was announced last week. Dr. Stentoft accepted a joint position at Western in January 2014 with the Departments of Economics, and Statistical and Actuarial Sciences. His work focuses on developing methods of modeling and pricing financial assets to improve market liquidity and allow financial markets to efficiently price and bear risk. The end goal is an increase in financial stability and a decrease in the likelihood of future market crashes or financial crises.
In this talk, we will present an estimation problem in multivariate linear model with multiple change-points which are unknown, under the scenario of uncertain prior information on the matrix of the regression coefficients. In particular, the target parameter is the matrix of the regression coefficients while the "change-points" are treated as nuisance parameters. We extend in three ways some recent methods in literature. First, an inference problem on a vector is extended to that for which the target parameter is a matrix. Second, we relax some assumptions, which are commonly given in literature, about the linear model with change-points, and we derive the joint asymptotic normality between the unrestricted and the restricted estimators. Third, we propose a class of shrinkage estimators which include as special cases the unrestricted and the restricted least square estimators as well as James-Stein type estimators. Further, in order to overcome some difficulties underlying the multidimensional aspect, we generalize some identities which are useful in risk evaluation of the shrinkage-type estimators.