# Biostatistics 602: Main Page

## Objective

In Winter 2013, Biostatistics 602 aims to provide students with a deep understanding of key concepts of statistical inference. Statistical inference methods instruct us how to use data to address substantive questions. In this course, we will study statistical point and interval estimation, hypothesis testing and basic asymptotic theory. We will primarily focus on classical frequentist’s view of statistical inference, and will briefly touch some basics of Bayesian inference.

## Prerequisites

Biostatistics 601 or equivalent knowledge of basic calculus and matrix algebra. In particular, students are expected to have knowledge of the following subjects: random variables, independence, characteristic and moment generating functions, common discrete and continuous distributions, expectations and higher order moments, random sampling. (approximately chapters 1-5.5 of Casella and Berger.)

## Textbook

• Statistical Inference, 2nd Edition, by Casella and Berger. (Required)
• Statistical Inference, by Garthwaite, Jolliffe and Jones. (Recommended)
• All of Statistics: A Concise Course in Statistical Inference, by Wasserman (Optional)
• Mathematical Statistics: Basics Ideas and Selected Topics, by Bickel and Doksum. (Optional)

## Class Schedule

Classes are scheduled for Tuesday and Thursdays, 1:00 - 3:00pm at USB 2260

Homework assignments will be given out at approximately every 1.5 weeks. Late submission will not be accepted unless the student obtains permission from the instructor. You are allowed to discuss homework problems with fellow students; however, you must write up the assignment on your own. Plagiarism will not be tolerated.

• Homework: 20%
• Midterm: 35%
• Final: 45%

## Topics

We will be primarily focusing on Chapter 6-10 of Casella and Berger. In particular, we will cover the following topics:

### Data Reduction (Week 1-4)

• Sufficiency principle (6.2)
• Sufficient statistics
• Complete statistics
• Ancillary statistics
• The exponential family of distributions
• Likelihood principle (6.3)

### Point Estimation (Week 5-10)

• Estimator construction (7.2)
• Moment estimator
• Maximum likelihood estimator
• Bayes estimator, and computational issues
• Evaluation of estimators (7.3)
• Unbiasedness
• Suﬃciency
• Asymptotic properties (10.1)
• Consistency
• Eﬃciency

### Hypothesis Testing (Week 11-13)

• Tests construction (8.2)
• Null and alternative hypotheses
• Composite hypotheses
• Likelihood ratio test
• Evaluation of tests (8.3):
• Neyman-Pearson lemma
• Asymptotic properties (10.3)

### Interval Estimation (Week 14-16)

• Interval construction (9.2)
• Evaluation of intervals (9.3)
• Asymptotic properties (10.4)

## Exams & Important Dates

• Midterm : Thursday February 21, 2013, in class
• Final : Thursday April 25, 2013, 4:00-6:00pm
• There will be no class on Thursday April 4th (instructor out of town)

## Office Hours

• Monday 4:00PM-5:00PM
• Thursday 4:30PM-5:00PM