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Old 01-26-2018, 02:11 PM
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Default Shapland Bootstrapping

How does random sampling with replacement from the residuals work? The text and CF or RF doesn't say much about it. It just gives original residuals and sampled residuals. What's the step between them?

Also, if you were to do 2nd, 3rd run of bootstrap, do you do random sampling from original residuals or residuals from the run prior?
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Old 01-26-2018, 02:54 PM
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If your triangle of residuals looks like this:

Code:
 0.04	0.65	-0.85
-0.10	0.28
 0.50
then number them, like maybe this:

Code:
1	4	6
2	5
3
then roll a die. if it comes up 6, then your sampled residual is -0.85. It gets more complex with heteroscedasticity and other issues.
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Old 01-26-2018, 02:56 PM
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Residuals always come from your original triangle.
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Old 01-26-2018, 03:53 PM
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Oh....so it can come from anywhere (except when residual is 0) regardless of row and column? Interesting....thanks!!
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Old 01-26-2018, 05:56 PM
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Quote:
Originally Posted by bjc2142 View Post
How does random sampling with replacement from the residuals work? The text and CF or RF doesn't say much about it. It just gives original residuals and sampled residuals. What's the step between them?

Also, if you were to do 2nd, 3rd run of bootstrap, do you do random sampling from original residuals or residuals from the run prior?
For each iteration (1, 2, ... 3,498...) the model will randomly select a triangle of residuals from the original triangle of standardized Pearson residuals excluding the corners that would show 0.

I find that it's a lot easier to visualize this by playing around with the "GLM Framework.xlsx" file that accompanies the Shapland paper. Definitely take a look at that.

You can download all the Shapland excel files from this link through casact.org:
http://www.casact.org/pubs/monograph...onograph04.zip
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Old 01-26-2018, 06:30 PM
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Thanks Steve! I guess it makes sense to resample from original triangle of residuals. If subsequent residuals are resampled from one run prior to that, in extreme case all the residuals in triangle could become just one number in later steps...Will definitely take a look at the excel file. It was scary looking beast the last time I tried to follow.
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