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#1
01-26-2018, 01:11 PM
 bjc2142 Member CAS Join Date: Aug 2014 Location: Boston Studying for nothing for fall '18 Favorite beer: Asahi Draft Posts: 734
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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#2
01-26-2018, 01:54 PM
 |B|rad Member CAS Join Date: Jul 2009 Posts: 1,001

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.
#3
01-26-2018, 01:56 PM
 |B|rad Member CAS Join Date: Jul 2009 Posts: 1,001

Residuals always come from your original triangle.
#4
01-26-2018, 02:53 PM
 bjc2142 Member CAS Join Date: Aug 2014 Location: Boston Studying for nothing for fall '18 Favorite beer: Asahi Draft Posts: 734

Oh....so it can come from anywhere (except when residual is 0) regardless of row and column? Interesting....thanks!!
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#5
01-26-2018, 04:56 PM
 SteveRoll Member CAS Join Date: Oct 2015 Posts: 80

Quote:
 Originally Posted by bjc2142 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.

http://www.casact.org/pubs/monograph...onograph04.zip
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Steve Roll, FCAS
www.RisingFellow.com
#6
01-26-2018, 05:30 PM
 bjc2142 Member CAS Join Date: Aug 2014 Location: Boston Studying for nothing for fall '18 Favorite beer: Asahi Draft Posts: 734

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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