MT427 Mathematical Statistics
Spring 2011

Prof.  Dan Chambers
Office:  365 Carney
chambers@bc.edu
617-552-3769 (email is more reliable)

Mathematical Statistics is a continuation of MT426 Probability or an equivalent (calculus-based) probability course. Whereas probability takes a given distribution and calculates the probability of seeing certain data values, statistics takes data and attempts to find the distribution that generates it, estimate parameters of the underlying distribution, and test hypotheses about those parameters.

Some of the topics we'll be covering this semester are: the central limit theorem, maximum likelihood estimation, method of moments estimation, confidence intervals, minimum-variance estimators, Cramer-Rao lower bound, sufficiency and consistency of estimators, hypothesis testing: binomial parameter, t test, Z test, generalized likelihood ratio, inferences about variances, two sample problems, goodness-of-fit tests, tests of independence and homogeneity, and nonparametric statistics.

Here is a link to the syllabus.

Here is a review of probability and some of the important distributions and their properties.

Office Hours: Mondays 12-1, Wednesdays 9-10, Fridays 3-4, or by appointment.

The text we'll use is An Introduction to Mathematical Statistics and Its Applications, 4th Edition, by Richard Larsen and Morris Marx. We'll finish chapter 4, then cover chapters 5-7, 9, 10, and some of 14.

 Week Monday Wednesday Friday Jan. 17-20 MLK Day 5.1 MLE introduction 5.2 MLE examples HW1 assigned (due January 28) Jan. 24-28 5.2 more MLE 5.2 more MLE MOM estimates 5.3 confidence intervals HW1 solutions Jan. 31- Feb. 4 class canceled 5.3 more confidence intervals 5.4 unbiasedness Feb. 7-11 5.5 CRLB 5.5 MVUE's HW2 solutions 5.6 sufficiency Feb. 14-18 5.6, 5.7 consistency 5.7 6.2 intro to hypothesis testing HW3 solutions Feb. 21-25 Exam 1 intro continued hyp. testing: means (known variance) Feb. 28- Mar. 4 hyp. testing: proportions (started) proportions (finished), P-values Type I and II errors, power Mar. 7-11 spring break spring break spring break Mar. 14-18 more on alpha, beta, power: sample size non-Normal data hyp. test vs CI estimators for mu, sigma Normal gamma function review Mar. 21-25 Chi Square distribution properties CI and hyp test for normal variance F and t distributions F and t distributions Mar. 28- Apr. 1 t test and CI's for means HW4 solutions two sample t test for means two sample test for variances Apr. 4- Apr. 8 two sample test for proportions HW5 solutions Exam 2 multinomial distributions HW6 Apr. 11-15 goodness of fit- known parameters goodness of fit-unknown parameters more examples Apr. 18-22 Patriot's Day intro to contingency tables HW7 solutions Easter break Apr. 25-29 Easter break Chi square test for independence sign test May 2-6 Wilcoxon signed rank test runs test for randomness