MATH4427 Mathematical Statistics
Fall 2018   MWF1   Stokes 295S

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Prof.  Dan Chambers
Office:  543 Maloney
chambers@bc.edu
2-3769 (email is more reliable)
www2.bc.edu/daniel-chambers

Mathematical Statistics is a continuation of MATH 4426 Probability or an equivalent (calculus-based) probability course. Whereas probability takes a given distribution and calculates the probability of seeing certain data values, statistics (among other things) 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.

Text: An Introduction to Mathematical Statistics and Its Applications, 5th Edition, by Richard Larsen and Morris Marx. We'll cover chapters 5-7, 9, 10, and some of 14.

Here is a link to the syllabus.

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

Office Hours: M2-3, W12-1, F11-12, or by appointment.

 August Topic, section HW assigned HW due/solns 27 5.1 MLE introduction 29 5.2 ML estimators 31 5.2 more MLE, MOM estimators HW#1 September 5 5.2, more MOM 7 5.3 confidence interval for mean HW1 10 5.3 CI for proportion, polls, sample size formulas 12 5.4 unbiased estimators HW#2 14 5.4 finished 17 5.5 CRL/MVUE's 19 5.5 continued 21 5.6 sufficiency HW2 24 5.7 consistency, Chebyshev's inequality HW#3 26 5.7 finished, 6.2 intro to hypothesis tests 28 6.2 tests for normal means October 1 class canceled HW3 3 Midterm 1  solutions 5 6.2/6.3  P values, proportions begun 10 6.3 proportions finished 12 6.4 start of Type I, II errors 15 6.4, 7.3 power,  gamma distributions HW#4 17 7.3 more gamma distribution 19 7.3 chi square distribution 22 7.3 more on chi square, CI for variance HW#4 24 7.3 hyp test for variance; 7.4 t distribution, CI and hyp test for one mean 26 7.4 examples; 29 9.2 two sample problem introduction;  t distribution and difference of means 31 9.2 two sample t test for means November 2 9.2, 9.3  CI for difference of two means, F distribution HW#5 5 9.3 two sample F test for variances 7 9.4 two sample test for proportions 9 9.5 two sample CI's, earthquake example HW#5 12 Midterm 2   solutions 14 10.2 multinomial distribution 16 10.3 goodness of fit: known parameters begun HW#6 19 10.3 ct'd 26 10.4 gof, unknown parameters 28 10.4, 10.5 contingency tables begun HW#6 30 10.5 tests for independence ct'd December 3 10.5, 14.2 sign test 5 14.2 sign test HW#7 7 class canceled 7 14.3 signed rank test HW#7 20 Final Exam 9:00 am