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How can we work together to promote better cultural understanding worldwide?

Qais Akbar Omar (GRS’16), a graduate student in the Creative Writing Program, has published a much-praised memoir, A Fort of Nine Towers: An Afghan Family Story. He recalls how the violence and tumult of civil war jolted his family, who, despite losing relatives, their home, and possessions, continued to nurture his wish to attend a university.

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Samuel Kou - Harvard University

4:00 pm on Thursday, November 15, 2012
5:00 pm on Thursday, November 15, 2012
MCS 148
Title: Optimal Shrinkage Estimation in Heteroscedastic Hierarchical Models. Abstract: Hierarchical models are powerful statistical tools widely used in scientific and engineering applications. The homoscedastic (equal variance) case has been extensively studied, and it is well known that shrinkage estimates, the James-Stein estimate in particular, have nice theoretical (e.g., risk) properties. The heteroscedastic (the unequal variance) case, on the other hand, has received less attention, even though it frequently appears in real applications. It is not clear of how to construct "optimal" shrinkage estimate. In this talk, we study this problem. We introduce a class of shrinkage estimates, inspired by Stein's unbiased risk estimate. We will show that this class is asymptotically optimal in the heteroscedastic case. We apply the estimates to real examples and observe excellent numerical results. This talk is based on joint work with Lawrence Brown and Xianchao Xie.