Mathematical Statistics Lecture

Recent Developments in Nonparametric Inference and Probability

No lecture on mathematical statistics is complete without the poetry of the Neyman-Pearson Lemma . The problem: test ( H_0: \theta = \theta_0 ) against ( H_1: \theta = \theta_1 ). The professor defines the likelihood ratio : mathematical statistics lecture

Let ( X_1, \dots, X_n ) be i.i.d. with mean ( \mu ) and finite variance ( \sigma^2 ). Then for large ( n ): [ \sqrtn(\barX - \mu) \xrightarrowd N(0, \sigma^2) ] Equivalently, ( \barX \approx N(\mu, \sigma^2/n) ). \sigma^2) ] Equivalently