STAT 513 (Theory of Statistical Inference)

Fall 2014

Instructor

David Hitchcock, associate professor of statistics

Syllabus

Syllabus: (Word document) or (pdf document)

Office Hours -- Fall 2014

Monday-Wednesday-Friday 1:15-2:30, Tuesdays 11:00-12:00 or please feel free to make an appointment to see me at other times.

Office: 209A LeConte College
Phone: 777-5346
E-mail: hitchcock@stat.sc.edu

Class Meeting Time

MWF 10:50 am - 11:40 am, Sloan College, Room 105

Current Textbook

Mathematical Statistics with Applications, 7th edition. (2008), by Wackerly, D., Mendenhall, W., and Scheaffer, R.

Course Description

513—Theory of Statistical Inference (3) (Prereq: STAT 512 with a grade of C or higher) Hypothesis testing, Neyman-Pearson lemma, likelihood ratio tests, power, theory of linear models including multiple linear regression and ANOVA, Bayesian inferences, advanced topics including survival analysis.

Purpose:

To provide a strong foundation in mathematical development of statistical inference methodology.

Course Notes

You are encouraged to print out these notes ahead of time and bring them to class.

Homework

Due DateProblems to be Graded on
Effort and Correctness 		Problems to be Graded
Solely on Effort
Friday, September 510.2(b,d,e), 10.20, 10.22, 10.26, 10.28(a), 10.38, 10.42 10.4(b,d)[NOTE: Switch the phrases "are/is error free"
with "contains an error" everywhere in problem 10.4], 10.6,
10.40
Friday, September 1210.56[Note: "attained significance level" = P-value],
10.58, 10.62, 10.64(c), 10.72(a), 10.76, 10.80, 10.82(a,c),
10.86, 10.88		 10.70(a, b-part [i]), 10.81, 10.89[show work!]
Monday, September 2910.96(a), 10.102, 10.106[see hint below], 10.111 10.91(a)[show work!], 10.94, 10.96(b)
Friday, October 1011.4, 11.8, 11.12, 11.15(b), 11.18(a),
11.32, 11.37[show work!], 11.40		 11.10, 11.15(a), 11.20, 11.22, 11.26[a,b,c,e], 11.28
Monday, November 311.45[show work!], 11.74(b,c)[see hint below], 11.75,
11.69, 11.72, 11.78, 11.90(b), 11.91[show work!]		 11.42, 11.68, 11.76, 11.77[show work!],
11.82(a), 11.83[show work!]
Friday, November 1411.48[also find a 95% CI for rho], 11.52, 13.70(a),
16.2, 16.8(a,b), 16.11(a,b,c,d), 16.15, 16.16		 11.54(b), 11.55, 11.87, 13.72, 16.8(c,d), 16.11(e,f)
Thursday, Dec. 4 by 2:00 p.m.16.21, 16.22, 16.24, 16.26[use R for these],
and Problems 1 and 2 here		 Problem 3 here

HINT for Problem 10.106: Use the fact that the maximum likelihood estimator for the common binomial proportion is simply the POOLED sample proportion (combining the wards), and the MLEs for the proportion in each ward are the sample proportions in each ward.

HINT for Problem 11.74: This problem is best done using R. You can enter the data into R using these commands:
y <- c(22.2,24.5,24.4,25.9,19.4,24.1,25.2,28.4,22.1,19.6,23.5,16.5,14.2,12.7,19.3,16)
x1 <- c(-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1)
x2 <- c(-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1)
x3 <- c(-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1)
x4 <- c(1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1)

NOTE: It appears that a few of the problem numbers in the "International Edition" of the textbook are switched around from the regular edition.
If you have the international edition, you might want to compare problem numbers with me or with a classmate who has the regular edition to make sure you're doing the problems assigned.
The problem numbers given above reflect the regular 7th edition.

Homework Solutions

[NOTE: Wording in problem 10.4 should read: "... Two ledger sheets are selected at random. If both are error-containing, we reject H_0. If one or more is error-free, we look at a third sheet. If the third sheet is error-containing, we reject H_0. In all other cases, we accept H_0."]

Some Additional Practice Problems

R Code for Class Examples

Project Information

Project Assignment: (Word document) or (pdf document)

Review Sheets

Formula Sheets

Exam Solutions

Exams