On 19 Mar 2004 at 9:54, Phillip Good wrote:
> I was merely commenting on your broad claim that MLE's are desirable
> for all distributions. What did you mean by that?
>
> "Robert J. MacG. Dawson" <[EMAIL PROTECTED]> wrote:Philip Good
> wrote:
>
> Alas, the desirable properties of an estimate arise for an MLE only if
> that distribution is normal.
>
(delayed reply)
You still did'nt inform us about your considerata! allowing you to
dispose of ML estimators. We are waiting. In the meantime I have a
question from one of your books
P. Good, permutation tests, 1. edition (in case there are more)
page 58, 4.4.1 Missing combinations.
There you are doing a somewhat mystical bootstrap without explaining
why some more usual variant does'nt work.
Code from R, entering the data, doing a usual stratifieb(by the tree
groups) bootstrap, and then your version, based on the last eq. on
page 59.
(Using the R boot package)
> Good <- data.frame(resp=scan(),
group=factor(c(rep("Y",5),rep("O",4),
+ rep("M", 3))))
1: 5640 5120 5780 4430 7230
6: 1150 2520 900 50
10: 7100
11: 11020
12: 13065
13:
Read 12 items
> summary(Good)
resp group
Min. : 50 M:3
1st Qu.: 2178 O:4
Median : 5380 Y:5
Mean : 5334
3rd Qu.: 7133
Max. :13065
# usual bootstrap:
> boot.Good1 <- function(data, ind) {
+ rs <- data[ind,1]
+ gr <- data[ind,2]
+ means <- tapply(rs, gr, mean)
+ gamma <- 0.5*means[2]+0.5*means[3]-means[1]
+ return(gamma) }
> boot1 <- boot(Good, boot.Good1, R=999, strata=Good$group)
> boot.ci(boot1)
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 999 bootstrap replicates
CALL :
boot.ci(boot.out = boot1)
Intervals :
Level Normal Basic
95% ( -9891, -4150 ) (-10233, -4456 )
Level Percentile BCa
95% (-9539, -3762 ) (-9338, -3496 )
Calculations and Intervals on Original Scale
Warning message:
Bootstrap variances needed for studentized intervals in:
boot.ci(boot1)
> boot.Good2 <- function(data, ind) {
+ x22 <- data[ind,1][10]
+ x21 <- data[ind,1][1]
+ x12 <- data[ind,1][6]
+ gamma <- 0.5*x12 + 0.5*x21 - x22
+ return(gamma) }
# Good's bootstrap:
> boot2 <- boot(Good, boot.Good2, R=999, strata=Good$group)
> boot.ci(boot2)
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 999 bootstrap replicates
CALL :
boot.ci(boot.out = boot2)
Intervals :
Level Normal Basic
95% (-5491, 4764 ) (-4500, 3070 )
Level Percentile BCa
95% (-10480, -2910 ) ( -8010, -2225 )
Calculations and Intervals on Original Scale
Warning : BCa Intervals used Extreme Quantiles
Some BCa intervals may be unstable
Warning messages:
1: Bootstrap variances needed for studentized intervals in:
boot.ci(boot2)
2: Extreme Order Statistics used as Endpoints in: norm.inter(t,
adj.alpha)
>
Note that the bootstrap confidence intervals are rather different.
Can you justify yout rather strange bootstrap?, it is not justified
in the book. Or explain why the moore usual one is mno good
for this example (not done in the book).
Cheers,
Kjetil Halvorsen
> Now, why would you say that? Until you say what "the" desirable
> properties of an estimate are I certainly can't confute your claim,
> but I am rather confident that if you *do* I can either find a
> counterexample or reassure myself that you desire some rather odd
> things from estimates that I needn't trouble myself about.
>
> So let's see your desiderata and we'll get this cleared up.
>
> -Robert
> .
> .
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>
>
> Phillip Good
> http.ms//www.statistician.usa
> "Never trust anything that can think for itself if you can't see where
> it keeps its brain." JKR
>
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