### Bootstrap

Bootstrap Methods

taught by Robert LaBudde

Aim of Course:

This online course, "Bootstrap Methods" covers the basic theory and application of the bootstrap family of procedures, with the emphasis on applications. After taking this course, participants will be able to use the bootstrap procedure to assess bias and variance, test hypotheses, and produce confidence intervals. The bootstrap is illustrated also for regression and time series procedures. Basic and improved bootstrap procedures are covered. See also the resampling course.

This course may be taken individually (one-off) or as part of a certificate program.

Course Program:

## WEEK 1: Introduction

- Wide range of application
- Historical notes
- Bias estimation
- Efron's patch data example
- Estimating other parameters of a distribution

## WEEK 2: Parameter Estimation

- Bias estimation (continued)
- Error rate estimation problems

- Confidence intervals and hypothesis test
- Percentile method confidence intervals
- Higher order bootstrap confidence intervals
- A 1-1 relationship between confidence intervals and hypothesis tests
- Problems with bootstrap confidence intervals for variances

## WEEK 3: Regression, Time Series, Which Methods?

- Linear Regression, bootstrap residuals or vectors
- Non-linear Regression
- A Quasi-optical experiment

- Nonparametric Regression
- Cox Model
- CART
- Bootstrap Bagging

- Time Series Analysis
- Model-based vs block resampling

- Bootstrap variants
- Bayesian bootstrap
- Smoothed bootstrap
- Parametric bootstrap
- Iterated bootstrap

- Number of repetitions (replications)

- Non-linear Regression

## WEEK4: Special Topics, Bootstrap Failures and Remedies

- Spatial data: kriging
- Subset selection
- Examples of Gong and Gunter

- p-value adjustment
- Process capability indices
- Bioequivalence
- Failure Due to Small Sample Size
- Failure Due to Infinite Moments and Remedy (introducing m-out-of-n bootstrap)
- Failure Due to Estimating Extremes and Remedies

HOMEWORK:

Homework in this course consists of short answer questions to test concepts and guided data analysis problems using software.

In addition to assigned readings, this course also has and an exam.

# Bootstrap Methods

Who Should Take This Course:

Statisticians and data analysts who perform statistical inference, or need to assess uncertainty in their data. Those working with data that does not meet the distributional requirements of standard statistical procedures, or with unusual statistics or complex estimators will find the course particularly useful.

See also: Introduction to Resampling Methods

Level:

intermediate/advanced

You should be familiar with introductory statistics. Try these self tests to check your knowledge.

Also: Introduction to Resampling, which provides a non-statistician's perspective on basic bootstrapping.

Use of statistical software is important in this course -- please read the software section below for additional information on software requirements.

Organization of the Course:

This course takes place online at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement:

About 15 hours per week, at times of your choosing.

Credit:

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

- You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
- You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
- You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's). For those successfully completing the course, CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

The required text for this course is *An Introduction to Bootstrap Methods with Applications to R* by Michael Chernick and Robert LaBudde.

PLEASE ORDER YOUR COPY IN TIME FOR THE COURSE STARTING DATE.

Software:

You must have a copy of R for the course. Click Here for information on obtaining a free copy. If you are not familiar with R, you should take one of statistics.com's "Introduction to R" courses: either R Programming - Introduction 1 or R for Statistical Analysis.

# Bootstrap Methods

September 15, 2017 to October 13, 2017September 14, 2018 to October 12, 2018