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In the gls fit shown below, the estimates of the standard deviation for each level of X are apparently given by the product of (1.000000, 3.913972, 10.684698, 11.350910, 26.476561, 27.255072) times the residual standard error of 0.04896334. How does one estimate the standard error of these estimated standard deviations (or variances)?

> m
    X     Y  F
1   1  1.07  1
2   1  1.01  1
3   1  0.99  1
4   1  1.09  1
5   1  0.94  1
6   1  1.00  1
7   1  1.01  1
8   1  0.98  1
9   1  1.00  1
10  1  1.03  1
11  4  3.66  4
12  4  3.75  4
13  4  3.77  4
14  4  3.92  4
15  4  4.08  4
16  4  3.99  4
17  4  3.95  4
18  4  4.10  4
19  4  3.88  4
20  4  4.04  4
21 10 10.13 10
22 10 10.20 10
23 10  9.77 10
24 10 10.28 10
25 10  8.71 10
26 10  9.79 10
27 10  9.82 10
28 10  9.85 10
29 10 10.07 10
30 10  9.63 10
31 20 20.22 20
32 20 19.46 20
33 20 19.02 20
34 20 20.06 20
35 20 20.94 20
36 20 19.92 20
37 20 19.96 20
38 20 20.04 20
39 20 19.67 20
40 20 19.96 20
41 30 31.04 30
42 30 31.40 30
43 30 31.84 30
44 30 30.77 30
45 30 32.13 30
46 30 31.17 30
47 30 30.36 30
48 30 29.95 30
49 30 30.74 30
50 30 30.67 30
51 40 41.14 40
52 40 40.29 40
53 40 42.77 40
54 40 38.36 40
55 40 39.17 40
56 40 39.61 40
57 40 40.73 40
58 40 39.42 40
59 40 40.72 40
60 40 40.24 40
> Fit.gls <- gls(Y ~ X,weights=varIdent(form = ~ 1 | F),data=m)
> summary(Fit.gls)
Generalized least squares fit by REML
  Model: Y ~ X 
  Data: m 
       AIC      BIC    logLik
  78.96207 95.44562 -31.48104

Variance function:
 Structure: Different standard deviations per stratum
 Formula: ~1 | F 
 Parameter estimates:
        1         4        10        20        30        40 
 1.000000  3.913972 10.684698 11.350910 26.476561 27.255072 
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What I was looking for is given by

intervals(Fit.gls)
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