##Statistics Seminar##\\ Department of Mathematical Sciences ^ **DATE:**|Thursday, Dec. 3, 2020 | ^ **TIME:**|1:15pm -- 2:15pm | ^ **LOCATION:**|Zoom meeting | ^ **SPEAKER:**|Mengyu Chen, Binghamton University | ^ **TITLE:**|An Empirical Likelihood Approach on Bivariate Random Variables| \\ **Abstract** Suppose Z_1, Z_2,..., Z_n are independent copies of Z=(X,Y), where X and Y-theta have the same marginal distributions. We want to test if theta equals some specific value, say 0. One way to do this is using two samples t test. There is another way by using empirical likelihood methods. Under some certain conditions, -2 log(R(theta)) has a limiting chi-square distribution. This method is much better by using the two samples t test. The empirical approach can later on be used to estimate the value of theta.