>> The bootstrap samples will also >> have less diverse values for the predictor variables. So it seems to >> me that the bootstrap results will NOT be a good guide to what is >> going on with the actual sample.
In article <[EMAIL PROTECTED]>, David Winsemius <[EMAIL PROTECTED]> wrote: >As I understand statistics, the goal is making some plausible statements >about what is likely in the world *outside* the sample. My understanding is >that bootstrap methods use the joint distribution of measured features of >the sample to create a plausible larger (neo-sampled) world. It seems to be >a realization of the concept of exchangeability. The idea of the bootstrap (as I understand it) is to mimic multiple samples of size N by sampling with replacement from the single actual sample of size N that is available. For this to be useful, these bootstrap samples need to resemble the original sample in the relevant aspects. But in a regression context, it's better to have N observations that are all for different values of the predictor variables than to have some of them be at the exact same predictor values as other observations. Since such exact coincidences are present in the bootstrap samples, it seems like they aren't very "plausible" in this context, and in particular, will tend to underestimate how much information can be obtained from an actual sample of size N. Of course, the usefulness of bootstrapping here may depend on what the end objective is... ---------------------------------------------------------------------------- Radford M. Neal [EMAIL PROTECTED] Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED] University of Toronto http://www.cs.utoronto.ca/~radford ---------------------------------------------------------------------------- . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
