CAS MA 782: HYPOTHESIS TESTING (SPRING 2012)

CAS MA 782: HYPOTHESIS TESTING (SPRING 2012)

Instructor: Dr. Surajit Ray

Department of Mathematics and Statistics

MCS 222, 111 Cummington Street, Boston, MA 02215

Phone: (617) 353-5209, Fax: (617) 353-8100

Class Time: Tue,Thu 12:30-2:00 PM

Class Room: MCS B31

Office Hours: TBD

Blackboard Login ( BU Students)

Department of Mathematics and Statistics

MCS 222, 111 Cummington Street, Boston, MA 02215

Phone: (617) 353-5209, Fax: (617) 353-8100

Class Time: Tue,Thu 12:30-2:00 PM

Class Room: MCS B31

Office Hours: TBD

Blackboard Login ( BU Students)

Course Description:

This is the second course in the MA781-782 sequence. This sequence is
designed to provide a solid foundation in mathematical statistics. In
MA782, we will build on the material we covered in MA781, and will
introduce fundamental approaches to hypothesis testing procedures,
including likelihood ratio based techniques and optimal classification
based on Neyman-Pearson Lemma. We will also discuss computational
approaches to hypothesis testing, and develop Bayesian approaches for
hypothesis testing.
Prerequisite:

The prerequisite for this course is MA781, and the course assumes strong
background in elementary probability theory (MA581 or equivalent).
Text:

- Casella, G. and Berger, R. L. Statistical Inference. 2 edition (June 18, 2001)

Publisher: Duxbury Press; ISBN-13: 978-0534243128

References:

- E. L. Lehmann, J. P. Romano: Testing statistical hypotheses

Springer New York 2005 (3rd edition), corr. 2nd printing 2006, XIV, 786 pages, ISBN: 0-387-98864-5 - Ferguson, T. S. Mathematical Statistics: A Decision Theoretic
Approach.

Published by Academic Press, New York, 1967.

Homework:

Homework will be assigned regularly during the course and a
due date will be announced. No late homework will be accepted. To receive full
credit for your solutions of the homework problems, all work must be shown.
Examinations:

There will be one midterm and one find. All exams are
required. Each test will be based on a combination of in-class and take-home
exams. A research project and in-class presentation will constitute a part of the
final exam. Exact dates of the exams will be announced later.
Grade Distribution:

Homework: 30%,
MIDTERM: 35%,
FINAL: 35%
Week-by-Week Syllabus:

Week | Topic |

1 | Introduction to Hypothesis Testing |

2 | Constructing Tests: Likelihood Ratio Tests (LRT) |

3 | Examples of LRT- Univariate and Multivariate |

4 | Likelihood ratio tests in the presence of nuisance parameters |

5 | Construction of tests using asymptotic distribution of LRT |

6 | Optimal Tests- Risk Function, Decision Rule |

7 | Neyman Pearson Lemma |

8 | Uniformly Most Powerful Tests, Examples of Monotone likelihood ratio |

9 | Karlin-Rubin Theorem, Uniformly Most Powerful Unbiased Tests |

10 | Confidence Interval Procedure for hypothesis tests |

11 | Bootstrap based hypothesis tests and Confidence Interval Procedures, Permutation Tests. |

12 | Bootstrap based inference in regression |

13 | Bayesian Hypothesis Testing |

14 | Review |

Please Note:

You are responsible for knowing,
and abiding by, the provisions of the GRS Academic Conduct Code,
which is posted at
*http://www.bu.edu/grs/academics/resources/adp.html.*Violations of the code are punishable by sanctions including expulsion from the University.