Math 541a - Introduction to Mathematical Statistics

Course Content:

Statistical models, Parametric families of distributions, multivariate distributions including the normal, order statistics.
Data reduction, sufficiency, completeness, exponential families.

Mixtures, inequalities, convergence concepts, sampling and derived distributions from a normal population.

Estimation: unbiased estimation, substitution principles, method of moments, least squares, maximum likelihood, asymptotics.

Comparison of estimators, optimality, information inequality, large sample behavior, consistency, convergence in distribution, asymptotic efficiency.

Time Permitting: Introduction to computationally intensive methods, EM algorithm, jackknife and bootstrap.

Prerequisites: Probability at the Math 505a level, or equivalent, multivariate calculus and linear algebra.

Instructor: Larry Goldstein, DRB 294, larry at math dot usc dot edu, (213) 740-2405
Office Hours: 10-11 Mondays, KAP Math Center
10-11 Wednesday and Friday in DRB 294

Teaching Assistant: Yu Zeng DRB 211
Office Hours (KAP math center): 11-12 on Tuesday and 4-5pm on Friday

Lecture: 39760R, MWF 11:00 - 11:50, KAP 163

Materials

Primary Text:
Statistical Inference, by Casella and Berger, 2nd Edition.

Supplemental References:
Statistical Inference by Garthwaite, Jolliffe and Jones, Oxford Scientific.
A Course in Large Sample Theory, by Ferguson.
Mathematical Statistics, by Bickel and Doksum
Asymptotic Statistics, by van der Vaart
Theory of Point Estimation, by E.L.Lehmann
Testing Statistical Hypotheses, by E.L.Lehmann
Linear Regression Analysis, by Seber and Lee

Notes : Order Statistics
Method of Moments
Estimating Equation Asymptotics

The Epic Story of Maximum Likelihood

Computationally Intensive Techniques:
Finite Markov Chains and Algorithmic Application. Olle Häggström
The EM Algorithm and Extensions. McLachlan and Krishnan
The Jackknife, the Bootstrap and Other Resampling Plans. Bradley Efron

Further References for Computational Methods in Statistics

Assignments from Text

Assignments and dates below are tenative, are not finalized until they appear in bold

Chapter 3: 2, 4, 5, 7, 11, 12, 14 due 1/25
Chapter 3: 18, 20, 25, 39, 41, 42, 45, Supplemental Assignment #1 due 2/11
Chapter 4: 14, 15, 18, 19, 20, 26, 39, 50, 54, 55, 56, 63 Supplemental Assignment #2 due 2/27
Chapter 5: 2, 8 (extra credit!), 10, 11, 12, 13, 19, 24, 31, 32, Supplemental Assignment #3 due 3/12
Chapter 5: 39, 40, 41, Chapter 6: 2, 3, 4, 15, 17, 18, 20 due 3/28
Chapter 7: 41, 42, 44, 45, 47, 49, 55, 57 due 4/11
Chapter 7: 3,6,7,9,11(replace theta by 1/theta in the given density),14, Supplemental Assignment #4 due 4/30

Exams and Grading Policy

Homework: 15%
There will be a penalty for late homework turned in within one week after the due date,
after which homework will not be accepted.

Two Midterms, each worth 25%, closed book
There is no need to have a sheet with formulas, or to have these memorized. A calculator will not be needed.

Midterm I: February 13th. Average 119, SD 42, 25th = 95, median = 120, 75th = 145, high = 200

Midterm II: March 26th, will cover up to (and including) sufficiency and completness.
Average = 127, SD= 35, 25th = 95, median = 125, 75th = 147, high = 195

Final Exam 35%, Wednesday, May 7, 11-1
The Final will be comprehensive, with an emphasis on material covered since Midterm II.

Important Dates

February 1st, last day to register, add, or to drop without mark of W

Arpil 11th, last day to drop a class with mark of W.

May 2nd, classes end.