Insightful Short Course: Bootstrap Methods and Permutation Tests
Bootstrap Methods and Permutation Tests
Course Description
Interest in computer based resampling methods has risen dramatically
over the past 20 years. Two resampling methods, bootstrapping and
permutation tests, has been applied successfully to areas of statistical
modelling where "traditional" standard errors, confidence
intervals and significance tests are unavailable or of doubtful
accuracy.
Even in situations where traditional methods are usually applied,
resampling methods are valuable as a validity check, and the answers
may surprise many experienced statisticians. For example, the old
rule of requiring sample sizes of at least 30 before applying Gaussian-based
methods is inaccurate in the presence of skewness. Resampling methods
offer graphical and numerical diagnostics for standard assumptions.
Resampling methods also offer practitioners greater flexibility
in modeling. They are no longer constrained to use simple statistics
such as sample means. They may use robust alternatives, and use
resampling for inferences.
Similarly, resampling offers the flexibility to handle complex
sampling situations, without the need for extensive analytical derivations.
The basic rule is to resample in a way consistent with the original
data collection. For example, when sampling from a finite population
one should use a finite-population resampling method.
Course Overview
This course begins with a graphical
approach to bootstrapping and permutation testing, illuminating
basic statistical concepts of standard errors, confidence intervals,
p-values and significance tests. We consider graphical and numerical
diagnostic checks for the validity of traditional Gaussian-based
inferences.
We then broaden our scope in three ways:
- To a wider variety applications, including
cases where bootstrapping fails, and how to recognize this
- To consider additional sampling methods,
including finite-sample and hierarchical sampling, and parametric
bootstrapping
-
To discuss additional resampling methods,
including the jackknife, influence methods, and cross-validation
The emphasis is on practical applications, with occasional notes
about the underlying theory. Examples will be analysed using the
statistical computing package S-PLUS, which has unparalleled resampling
capabilities and the flexibility to deal with non-standard applications.
Who Should Attend?
Statisticians faced with inferential problems
where the use of standard results may be questionable or not available.
Familiarity with S-PLUS is not necessary.
How You Will Benefit
You will learn how to use resampling methods to for inferences,
or to check the accuracy of standard methods, for a variety of statistical
applications. Many attendees will gain a better understanding of
statistical concepts such as standard errors, Gaussian approximations,
and p-values.