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Statistical Machine Learning Seminar
Hosted by Department of Mathematical Sciences
Abstract
Consider that we are observing iid copies (Xi,Yi)ni=1 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, \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.