beamer-tu-logo

Stat 609: Mathematical Statistics I (Fall Semester, 2014) Lecture 0: Introduction

Course information

Instructor  Professor Jun Shao TA Ms Cuicui Qi
Office  1235A MSC  1335C MSC
Phone  608-262-7938  608-263-5948
Email  shao@stat.wisc.edu  cuicui@stat.wisc.edu
Office hours 9:50-10:50am M  12:30-2:00pm R

12:00-1:00pm W or by appointment

Lecture  11:00-11:50am MWF (room 133 MSC)
Discussion 2:25-3:40pm F (room 1313 Sterling)

Discussions taught by TA

beamer-tu-logo

Textbook

Book  Statistical Inference, 2nd edition
Authors  George Casella and Roger L. Berger
Publisher  Brooks/Cole Cengage Learning
Topics covered Chapters 1-6
Syllabus  See the list of topics
Recommended Mathematical Statistics (1977, Bickel and Doksum)
reading books An Introduction to Probability Theory and

Mathematical Statistics (1976, Rohatgi)

Homework Assignments

In each lecture, there are 2-4 homework problems selected from the textbook. Problems are assigned in groups with a specified due date. Some or all problems are graded by the TA and a solution will be provided.

UW-Madison (Statistics)  Stat 609 Lecture 0  2014  2 / 7

beamer-tu-logo

Exam Schedule

1st exam  11:00am-12noon on Oct 3, 2014 (in class)

Cover Chapters 1-2

2nd exam 11:00am-12noon on Nov 7, 2014 (in class)

Cover Chapters 3-4

Final exam 2:45-4:45pm on Dec 17, 2014 (may be changed)

Cover Chapters 1-4 (30%) and Chapters 5-6 (70%)

Note  All exams are closed-book

You may bring 1 sheet (2 pages) of notes

Course Grades

Assignments 20 points  Grades A (90-100)
1st exam  20 points  AB (80-89)
2nd exam  20 points  B (70-79)
Final exam  40 points  BC (60-69)
Total  100 points  C(50-59)

......

Adjustments may be made

UW-Madison (Statistics)  Stat 609 Lecture 0  2014  3 / 7

beamer-tu-logo

Required Mathematics Linear algebra

Vectors c = (c_{1},...,c_{k}), row or column, transpose c′ Matrices A, its dimension, transpose A′ Vector/matrix addition and multiplications: c′A, A + B, AB, ... Positive and non-negative definite matrices and their simple properties.

Calculus, advanced calculus or mathematical analysis

Functions (univariate or multivariate), domain and range Limits (as n → ∞ or as x → x_{0}), ϵ-N or ϵ-δ arguments Continuity and differentiability of functions Right-continuous, left-continuous Right-derivative, left-derivative Integration with finite or infinite integral limits Existence of an integral: e.g., ∫_{−∞}^{∞} |g(x)|dx = ∞ or a finite number?

UW-Madison (Statistics)  Stat 609 Lecture 0  2014  4 / 7

beamer-tu-logo

Calculus, advanced calculus or mathematical analysis

Series: when does ∑ _{n=1}^{∞}a_{n} converge? Geometric series:

\frac{1}{1 − x} = ∑_{t=0}^{∞}x^{t} |x| < 1

Power series:

e^{x} = ∑_{t=0}^{∞} \frac{x^{t}}{t!} |x| < ∞

Infinity

For any real number x, ∞ + x = ∞, x ∞ = ∞ if x > 0, x ∞ = −∞ if x < 0, and 0∞ = 0; ∞ + ∞ = ∞; ∞^{a} = ∞ for any a > 0; x/0 = ∞ if x > 0 and x/0 = −∞ if x < 0; ∞ − ∞ or ∞/∞ or 0/0 is not defined.

Mathematical induction

Prove a statement involving n is true for any fixed n = 1,2,3,... (but not n → ∞)

UW-Madison (Statistics)  Stat 609 Lecture 0  2014  5 / 7

beamer-tu-logo

Knowledge in probability and mathematical statistics

It is not required, but is very helpful if you took a course in probability and statistics previously Sets, subsets and set operations

Purposes of Stat 609-610

Learning statistical concepts and knowledge (together with Stat 571-572 or 671-672 sequence) Training at the level of the Mater of Science in Statistics

Stat 609: Basic probability tools useful in statistics (Chapters 1-5) and data reduction principles (Chapter 6) Stat 610: Basic topics in statistical inference (Chapters 7-12)

Training in derivations and simple proofs Preparation for a PhD level study in statistics

beamer-tu-logo

Suggestions for studying

Take class notes wisely. Do not be afraid of asking questions to the instructor and TA, either during or after the class. Read the relevant part of the textbook carefully after each lecture. Do the related homework problems after each lecture. Do not delay the work until the due date or the day before the due date. Do homework problems independently. Group discussions are encouraged, but you should do your own work. If you have time, try to do more problems from the textbook, which contains many good problems but I don’t want to assign all. Study the graded problems from the TA, and the solution. It is a good idea to study a different solution to a (complicated) problem. Review the material before each exam (there will be a review class prior to each exam) and carefully prepare the one sheet notes for each exam. Menage the time wisely in the exam.

UW-Madison (Statistics)  Stat 609 Lecture 0  2014  7 / 7