##Statistics Seminar##\\ Department of Mathematical Sciences ^ **DATE:**|Thursday, August 29, 2019 | ^ **TIME:**|1:15pm -- 2:15pm | ^ **LOCATION:**|WH 100E | ^ **SPEAKER:**|Qiqing Yu, Binghamton University | ^ **TITLE:**| A Note On Application Of The Kullback-Leibler Information Inequality | \\ **Abstract** One often makes use of Shannon-Kolmogorov inequality in proving the consistency of the maximum likelihood estimator (MLE). The approach does not work when E(\ln f(X)) does not exist, where f is the density function of the random variable X. We consider several parametric distribution families where E(\ln f(X)) does not exist. We make use of the Kullback-Leibler (K-L) Information inequality in proving that the MLE is consistent.