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--- seminars:sml:160412 [2016/04/08 16:56] – qiao
+++ seminars:sml:160412 [2016/04/08 16:56] (current) – qiao
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+<WRAP centeralign>##Statistical Machine Learning Seminar##\\ Hosted by Department of Mathematical Sciences</WRAP>
+~~META:title=April 19, 2016~~
+  * Date: Tuesday, April 12, 2016
+  * Time: 12:00-1:00
+  * Room: WH-100E
+  * Speaker: Ruiqi Liu (Mathematical Sciences)
+  * Title: TBA
+<WRAP center box 80%>
+<WRAP centeralign>**//Abstract//**</WRAP>
+Consider that we are observing iid copies $(X_i, Y_i)_{i=1}^n$ from random vector $(X, Y)$.  According to some historical information, the marginal distributions of $X$ and $Y$ are known, but the joint distribution is unclear. A problem of interest is to estimate $\exp[h(X,Y)]$ for some measurable function $h$. This is of application value. For example, in insurance industry,  some life insurance policies will cover both husband and wife . Let $X,Y$ be the left life time of husband and wife after signing the policy and $X, Y$ are usually dependent. The company is able to obtain the marginal distributions of $X$ and $Y$ from historical records. Often, the values of interest are $\min(X, Y)$, $\max(X, Y)$ or their distributions. This paper provides an empirical likelihood estimator to solve this problem. Some nice properties of our estimator are supported by theoretical analysis and simulation results.
+</WRAP>