Testing of hypotheses: Randomized and non-randomized tests. Power and size of a test. Most powerful (MP) test. Neyman–Pearson lemma. Uniformly most powerful (UMP) tests, Monotone likelihood ratio (MLR) property and construction of UMP tests for the families of distributions possessing MLR property, Applications. Non- existence of UMP tests for two-sided alternatives.
Similar tests and unbiased tests. Statements of theorems for the construction of UMPU tests for exponential families of distributions and their application to samples from normal distribution leading to t, $\chi^2$ and F tests – one and two-sample problems. Student’s t- test for correlation coefficient.
Casella G. and Berger R.I. (2002) Statistical Inference, Duxbury Press, Belmont, California, USA
Siva Athreya, Deepayan Sarkar and Steve Tanner, Probability and Statistics with Examples using R
Office Hours: Friday 9-10am or by appointment.
Class time: Friday 10:15am -12:15pm, in Lecture hall 1, Statistics Department, Bangalore University.
Grading: Quizes (5 points), (10 points Test), (35 points Final)
There will be Homework every week
and a short quiz on Friday morning.
Studying and Homework: The course requires at least two hours of study for each hour of class time. Homework will be posted on the web. It is imperative that you try, (and write up solutions for), the homework problems {\em BEFORE} their respective due dates. The problems given are a small selection so please do try other problems for practice from the text. You are encouraged to work together on solving the problems.
Feedback: Please feel free to drop by during office hours, to clear up difficulties or to just discuss mathematics. I would appreciate feedback from you as the course progresses. If there are suggestions/clarifications that you have then feel free to ask me.
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Homework Set |
Class Board Photos |
Notes |