This function returns resampled data or indices created by balanced bootstrap
or bootknife resampling.
-- Function File: BOOTSAM = boot (N, NBOOT)
-- Function File: BOOTSAM = boot (X, NBOOT)
-- Function File: BOOTSAM = boot (..., NBOOT, LOO)
-- Function File: BOOTSAM = boot (..., NBOOT, LOO, SEED)
-- Function File: BOOTSAM = boot (..., NBOOT, LOO, SEED, WEIGHTS)
'BOOTSAM = boot (N, NBOOT)' generates NBOOT bootstrap samples of length N.
The samples generated are composed of indices within the range 1:N, which
are chosen by random resampling with replacement [1]. N and NBOOT must be
positive integers. The returned value, BOOTSAM, is a matrix of indices,
with N rows and NBOOT columns. The efficiency of the bootstrap simulation
is ensured by sampling each of the indices exactly NBOOT times, for first-
order balance [2-3]. Balanced resampling only applies when NBOOT > 1.
'BOOTSAM = boot (X, NBOOT)' generates NBOOT bootstrap samples, each the
same length as X (N). X must be a numeric vector, and NBOOT must be
positive integer. BOOTSAM is a matrix of values from X, with N rows
and NBOOT columns. The samples generated contains values of X, which
are chosen by balanced bootstrap resampling as described above [1-3].
Balanced resampling only applies when NBOOT > 1.
Note that the values of N and NBOOT map onto int32 data types in the
boot MEX file. Therefore, these values must never exceed (2^31)-1.
'BOOTSAM = boot (..., NBOOT, LOO)' sets the resampling method. If LOO
is false, the resampling method used is balanced bootstrap resampling.
If LOO is true, the resampling method used is balanced bootknife
resampling [4]. The latter involves creating leave-one-out (jackknife)
samples of size N - 1, and then drawing resamples of size N with
replacement from the jackknife samples, thereby incorporating Bessel's
correction into the resampling procedure. LOO must be a scalar logical
value. The default value of LOO is false.
'BOOTSAM = boot (..., NBOOT, LOO, SEED)' sets a seed to initialize
the pseudo-random number generator to make resampling reproducible between
calls to the boot function. Note that the mex function compiled from the
source code boot.cpp is not thread-safe. Below is an example of a line of
code one can run in Octave/Matlab before attempting parallel operation of
boot.mex in order to ensure that the initial random seeds of each thread
are unique:
• In Octave:
pararrayfun (nproc, @boot, 1, 1, false, 1:nproc)
• In Matlab:
ncpus = feature('numcores');
parfor i = 1:ncpus; boot (1, 1, false, i); end;
'BOOTSAM = boot (..., NBOOT, LOO, SEED, WEIGHTS)' sets a weight
vector of length N. If WEIGHTS is empty or not provided, the default
is a vector of length N, with each element equal to NBOOT (i.e. uniform
weighting). Each element of WEIGHTS is the number of times that the
corresponding index (or element in X) is represented in BOOTSAM.
Therefore, the sum of WEIGHTS must equal N * NBOOT.
Bibliography:
[1] Efron, and Tibshirani (1993) An Introduction to the
Bootstrap. New York, NY: Chapman & Hall
[2] Davison et al. (1986) Efficient Bootstrap Simulation.
Biometrika, 73: 555-66
[3] Booth, Hall and Wood (1993) Balanced Importance Resampling
for the Bootstrap. The Annals of Statistics. 21(1):286-298
[4] Hesterberg T.C. (2004) Unbiasing the Bootstrap—Bootknife Sampling
vs. Smoothing; Proceedings of the Section on Statistics & the
Environment. Alexandria, VA: American Statistical Association.
boot (version 2024.04.24)
Author: Andrew Charles Penn
https://www.researchgate.net/profile/Andrew_Penn/
Copyright 2019 Andrew Charles Penn
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see http://www.gnu.org/licenses/
The following code
% N as input; balanced bootstrap resampling with replacement boot(3, 20, false)
Produces the following output
ans =
Columns 1 through 6:
2 3 3 2 2 2
3 1 3 1 2 3
2 1 3 3 2 1
Columns 7 through 12:
1 1 3 1 3 3
2 2 2 1 2 1
2 3 1 2 1 2
Columns 13 through 18:
2 1 2 2 3 3
2 2 3 3 1 1
3 1 1 1 2 3
Columns 19 and 20:
1 1
3 3
3 1
The following code
% N as input; (unbiased) balanced bootknife resampling with replacement boot(3, 20, true)
Produces the following output
ans =
Columns 1 through 6:
2 3 2 2 3 1
2 1 1 2 3 2
3 3 1 2 3 1
Columns 7 through 12:
3 1 2 2 1 2
2 1 1 3 3 1
3 1 2 2 3 2
Columns 13 through 18:
2 3 1 2 1 2
3 3 1 2 1 1
3 1 1 3 3 1
Columns 19 and 20:
3 3
1 2
3 2
The following code
% N as input; balanced resampling with replacement; setting the random seed boot(3, 20, false, 1) % Set random seed boot(3, 20, false, 1) % Reset random seed, BOOTSAM is the same boot(3, 20, false) % Without setting random seed, BOOTSAM is different
Produces the following output
ans =
Columns 1 through 6:
3 3 3 3 1 2
3 1 2 2 3 1
3 2 3 1 3 1
Columns 7 through 12:
3 3 1 1 2 2
3 1 2 2 3 3
1 1 3 1 2 3
Columns 13 through 18:
1 2 2 2 1 2
2 3 3 3 3 1
2 1 2 2 2 1
Columns 19 and 20:
1 1
1 2
2 1
ans =
Columns 1 through 6:
3 3 3 3 1 2
3 1 2 2 3 1
3 2 3 1 3 1
Columns 7 through 12:
3 3 1 1 2 2
3 1 2 2 3 3
1 1 3 1 2 3
Columns 13 through 18:
1 2 2 2 1 2
2 3 3 3 3 1
2 1 2 2 2 1
Columns 19 and 20:
1 1
1 2
2 1
ans =
Columns 1 through 6:
3 2 2 3 2 3
1 3 1 1 2 3
1 3 3 1 1 1
Columns 7 through 12:
1 2 2 3 1 2
3 3 1 2 1 1
2 3 2 2 2 1
Columns 13 through 18:
3 1 2 3 2 3
2 1 3 1 1 3
2 3 3 1 1 2
Columns 19 and 20:
2 3
3 2
2 1
The following code
% Vector (X) as input; balanced resampling with replacement; setting weights x = [23; 44; 36]; boot(x, 10, false, 1) % equal weighting boot(x, 10, false, 1, [20;0;10]) % unequal weighting, no x(2) in BOOTSAM
Produces the following output
ans =
Columns 1 through 6:
44 23 23 36 44 23
36 23 36 23 44 36
36 36 23 44 23 44
Columns 7 through 10:
44 36 36 23
36 23 44 44
23 36 44 44
ans =
Columns 1 through 6:
23 23 23 36 23 23
36 23 36 23 23 36
36 36 23 23 23 23
Columns 7 through 10:
23 36 36 23
36 23 23 23
23 36 23 23
The following code
% N as input; resampling without replacement; 3 trials boot(6, 1, false, 1) % Sample 1; Set random seed for first sample only boot(6, 1, false) % Sample 2 boot(6, 1, false) % Sample 3
Produces the following output
ans =
4
2
3
5
4
6
ans =
4
3
4
6
6
2
ans =
5
6
3
4
1
6
Package: statistics-resampling