Lecture 9—Wednesday, Sept. 17, 2003

What was covered?

Overview of Estimation

In class and/or in the textbook, we've dealt with four types of estimation methods

  1. Method of moments (also called plug-in) estimators.
  2. Estimators based on non-statistical theory.
  3. Maximum likelihood estimators (mles)
  4. Least squares estimators.

Note: the sample mean is a method of moments estimator, a maximum likelihood estimator (under virtually all probability models), and a least squares estimator. In a least squares sense, it is the value of c that minimizes the expression .

Bootstrapping

Parametric Bootstrap

Nonparametric Bootstrap

Bootstrap Confidence Intervals

There are five basic bootstrap confidence intervals implemented in the boot library of R. I describe each in turn.

Normal (Standard) Bootstrap Confidence Interval: type='norm'

Percentile Bootstrap Confidence Interval: type='perc'

Basic Bootstrap Confidence Interval: type='basic' (not covered in lecture)

but we use

to actually find them and hope that they're close to the ones we actually want.

Studentized-t (Percentile-t) Bootstrap Confidence Interval: type='stud'

where is the bootstrap estimate of the standard error of . Notice that the quantiles of the bootstrapped t are used in what is perhaps the reversed order from what you might expect.

Bias-corrected and Accelerated Bootstrap Confidence Interval: type='bca'

Vocabulary


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Jack Weiss
Phone: (919) 962-5930
E-Mail: jack_weiss@unc.edu
Address: Curriculum in Ecology, Box 3275, University of North Carolina, Chapel Hill, 27516
Copyright © 2003
Last Revised--Sept 23, 2003
URL: http://www.unc.edu/courses/2003fall/biol/145/001/docs/lectures/Sep17.html