# Overview

Statistics 7301 is a course on the fundamentals of statistical theory and is intended for second-year Ph.D. students in statistics. The course is based in part on chapters 2–4,8–9 of the required book Theoretical Statistics: Topics for a Core Course, chapters 2 and 6 of the required book All of Nonparametric Statistics, and notes provided by the instructor. The topics of the course include:

1. Fundamentals
• Statistics, sufficiency, and completeness
• Exponential families
• Rao-Blackwell theorem
• Fisher information
2. Methods of estimation
• Unbiased estimation
• Maximum likelihood
• Minimum contrast estimation
3. Asymptotic approximations (a.k.a. large sample theory)
• Consistency
• Delta method
• Asymptotic normality and efficiency
4. Nonparametric estimation
• Estimating the CDF and statistical functionals
• Influence functions and nonparametric Delta method
• Density estimation

# Textbook

The in-class lectures and notes are the canonical source for the course. The following books are also required for supplemental reading:

• Keener, R.: Theoretical Statistics: Topics for a Core Course. Springer.
• Wasserman, L.: All of Nonparametric Statistics. Springer.

The notation and nomenclature used in lecture and the depth of coverage of material will occasionally deviate from these books. The instructor will try to alert students to these differences, but ultimately students are expected to pay attention to these differences themselves.

The follows books are optional references:

# Prerequisites

Statistics 6802, or permission of the instructor, and concurrent enrollment in Statistics 7201. Mathematical analysis and probability theory are the primary tools of statistical theory. Students are expected to be able to read and write mathematical proofs.

There will be homework, three in-class exams, a final exam, and scribing.

• 15% Homework
• 15% Exam 1 (September 25)
• 15% Exam 2 (October 20)
• 15% Exam 3 (November 17)
• 40% Final exam (December 11)
• Mandatory scribing of max(2, floor(36/n)) lectures (where n is the number of students and floor(x) is the largest integer less than or equal x)

Inform the instructor of any scheduling conflicts at least two weeks in advance.

## Homework

Homeworks will generally be assigned on a weekly basis and are due in class on the due date. If you cannot attend class on the due date of the homework, then either ask a classmate to submit the homework for you or place the homework under my office door in advance. Late homework will not be accepted and returned without grading.

## Exams

All exams are closed book. Each of exams 1–3 covers the material presented since the previous exam (approximately 3–4 weeks worth). The final exam is cumulative.

## Scribing

Students will be required to scribe max(2, floor(36/n)) lectures using LaTeX and a template provided by the instructor. Additional instructions will be given by the instructor.