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