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Bootstrap Methods

Dr. Michael Chernick

Aim of Course:

This course 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.

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.

For those enrolled in Professional Advancement Programs, this is a required or elective course in the following Programs:

  • Statistics for Environmental Science - elective
  • Statistics for Social Sciences - elective
  • Data Mining - elective
  • Biostatistics (controlled trials) - elective
  • Biostatistics (epidemiology) - elective

Course Program:

The course is structured as follows

SESSION 1: Introduction
  • Wide range of application
  • Historical notes
  • Bias estimation
    • Efron's patch data example
    • Estimating other parameters of a distribution
SESSION 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
SESSION 3: Regression, Time Series, Which Methods?, Efficient Simulation
  • Linear Regression, bootstrap residuals or vectors
  • Non-linear Regression
    • A Quasi-optical experiment
  • Time Series Analysis
    • Model-based vs block resampling
  • Bootstrap variants
    • Bayesian bootstrap
    • Smoothed bootstrap
    • Parametric bootstrap
    • Iterated bootstrap
  • Number of repetitions (replications)
  • Variance Reduction Methods
SESSION 4: Special Topics, Bootstrap Failures and Remedies (discussion only, no exercises)
  • Spatial data – kriging
  • Subset selection
  • 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

The Instructor:

Michael Chernick is the author of Bootstrap Methods: A Practitioner's Guide (Wiley, 1999), with the second edition title Bootstrap Methods: A Guide for Practitioners and Researchers (Wiley, forthcoming 2007). He is also the coauthor of Introductory Biostatistics for the Health Sciences: Modern Methods including Bootstrap (Wiley, 2002). He is a Fellow of the American Statistical Association and the author of more than 30 journal articles. He is the winner of the Wolfowitz Prize in 1983 and is a Past President of the Southern California Chapter of the American Statistical Association. He has taught at California State University and the University of Southern California, has given several previous short courses on bootstrap methods and has also worked in the aerospace, medical device and pharmaceutical industries. Dr. Chernick has a Ph.D. in statistics from Stanford University.

Organization of the Course:

The course takes place over the internet, at statistics.com. 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. The course is scheduled to take place over 4 weeks, and typically requires 10-15 hours per week. 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 and work through exercises. Discussion among participants is encouraged. The instructor will provide answers and comments.

Certificates and Grades:

You may be interested only in learning the material presented, and not be concerned with grades or certificates. Or you may be enrolled in a statistics.com Professional Advancement Program that requires demonstration of proficiency in the subject, in which case your work will be assessed for purposes of issuing a grade. Or you may require only a "Certificate of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's). As you begin the class, you will be asked to specify your category.

Credit:

This course offers continuing education units (CEU's). For those successfully completing the course (generally this means marks of 50% or better on the homework), 5.0 CEU's and a certificate will be issued by statistics.com, upon request.

Dates:

Sep. 26 - Oct. 24, 2008
Mar. 27 - Apr. 24, 2009
Click here to be notified of future course offerings.

Participants gain access to the online materials on the first day of the course, and typically spend about 10-15 hours per week (at their convenience). You retain full access to course materials, including discussion board, for two weeks after the course closing date.

Level:

intermediate/advanced

Prerequisite:

The equivalent of Introduction to Statistics I: Inference for a Single Variable, and Introduction to Statistics II: Working with Bivariate Data (and, if necessary before these courses, Introduction to Statistics for Beginners or Survey of Statistics for Beginners). Though not a prerequisite, Introduction to Resampling will also be useful -- it 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.

Course Text:

Bootstrap Methods: A Guide for Practitioners and Researchers, 2nd edition by Michael Chernick, available from Wiley here. Please order the second edition. A 15% discount if you order from the above link.

Software:

This course has illustrations and exercises with solutions and some pointers using both Resampling Stats for Excel and R. Most of the problems can be done in Resampling Stats; some will require R or a similar programming environment. Resampling Stats is a special purpose program that can be downloaded and tried ahead of time and learned as part of the course; a license extension will be provided to course participants on the first day of the class. R is a comprehensive statistical programming language; if you are going to do the course in R, you should be familiar with that program before starting the course (statistics.com offers severl courses in the use of R). S-PLUS is also ideal for resampling, and the instructions for R can also be used for S-PLUS. Stata is another program that provides a good environment for resampling, but help is not available for Stata. Click here for download information for these and other software packages that offer free or nominal cost versions that may be used in statistics.com courses.

Registration:

Register Online - $449
Register Online (academic) - $349 (you must be affiliated with a college, university or high school)

Add $50 service fee if you require a prior invoice, or if you need to submit a purchase order or voucher, pay by wire transfer or EFT, or refund and reprocess a prior payment. Please use this printed registration form, for these and other special orders.

Note: Courses may fill up at any time and registrations are processed in the order in which they are received. Your registration will be confirmed for the first available course date, unless you specify otherwise.