bootstrp
-
Balanced bootstrap resampling.
+ Bootstrap resampling.
-- Function File: BOOTSTAT = bootstrp (NBOOT, BOOTFUN, D)
-- Function File: BOOTSTAT = bootstrp (NBOOT, BOOTFUN, D1, ..., DN)
- -- Function File: BOOTSTAT = bootstrp (..., 'seed', SEED)
-- Function File: BOOTSTAT = bootstrp (..., 'Options', PAROPT)
+ -- Function File: BOOTSTAT = bootstrp (..., 'Weights', WEIGHTS)
+ -- Function File: BOOTSTAT = bootstrp (..., 'seed', SEED)
+ -- Function File: BOOTSTAT = bootstrp (..., 'loo', LOO)
+ -- Function File: BOOTSTAT = bootstrp (..., D1, ..., DN, 'match', MATCH)
-- Function File: [BOOTSTAT, BOOTSAM] = bootstrp (...)
- BOOTSTAT = bootstrp (NBOOT, BOOTFUN, D) draws NBOOT bootstrap resamples
- from the data D and returns the statistic computed by BOOTFUN in BOOTSTAT
- [1]. bootstrp resamples from the rows of a data sample D (column vector
- or a matrix). BOOTFUN is a function handle (e.g. specified with @), or a
- string indicating the function name. The third input argument is data
- (column vector or a matrix), that is used to create inputs for BOOTFUN.
- The resampling method used throughout is balanced bootstrap resampling
- [2-3].
-
- BOOTSTAT = bootstrp (NBOOT, BOOTFUN, D1,...,DN) is as above except that
- the third and subsequent numeric input arguments are data vectors that
- are used to create inputs for BOOTFUN.
+ 'BOOTSTAT = bootstrp (NBOOT, BOOTFUN, D)' draws NBOOT bootstrap resamples
+ with replacement from the rows of the data D and returns the statistic
+ computed by BOOTFUN in BOOTSTAT [1]. BOOTFUN is a function handle (e.g.
+ specified with @) or name, a string indicating the function name, or a
+ cell array, where the first cell is one of the above function definitions
+ and the remaining cells are (additional) input arguments to that function
+ (after the data argument(s)). The third input argument is the data
+ (column vector, matrix or cell array), which is supplied to BOOTFUN. The
+ simulation method used by default is bootstrap resampling with first order
+ balance [2-3].
- BOOTSTAT = bootstrp (..., 'seed', SEED) initialises the Mersenne Twister
- random number generator using an integer SEED value so that bootci results
- are reproducible.
+ 'BOOTSTAT = bootstrp (NBOOT, BOOTFUN, D1,...,DN)' is as above except that
+ the third and subsequent input arguments are data are used to create
+ inputs for BOOTFUN.
- BOOTSTAT = bootstrp (..., 'Options', PAROPT) specifies options that govern
- if and how to perform bootstrap iterations using multiple processors (if
- the Parallel Computing Toolbox or Octave Parallel package is available).
- This argument is a structure with the following recognised fields:
+ 'BOOTSTAT = bootstrp (..., 'Options', PAROPT)' specifies options that
+ govern if and how to perform bootstrap iterations using multiple
+ processors (if the Parallel Computing Toolbox or Octave Parallel package).
+ is available This argument is a structure with the following recognised
+ fields:
o 'UseParallel': If true, use parallel processes to accelerate
bootstrap computations on multicore machines.
Default is false for serial computation. In MATLAB,
@@ -57,10 +59,43 @@ bootstrp
has already been started.
o 'nproc': nproc sets the number of parallel processes
- [BOOTSTAT, BOOTSAM] = bootstrp (...) also returns BOOTSAM, a matrix of
- indices from the bootstrap. Each column in BOOTSAM corresponds to one
- bootstrap sample and contains the row indices of the values drawn from
- the nonscalar data argument to create that sample.
+ 'BOOTSTAT = bootstrp (..., D1, ..., DN, 'match', MATCH)' controls the
+ resampling strategy when multiple data arguments are provided. When MATCH
+ is true, row indices of D1 to DN are the same (i.e. matched) for each
+ resample. This is the default strategy when D1 to DN all have the same
+ number of rows. If MATCH is set to false, then row indices are resampled
+ indpendently for D1 to DN in each of the resamples. When any of the data
+ D1 to DN, have a different number of rows, this input argument is ignored
+ and MATCH is enforced to have a value of false.
+
+ 'BOOTSTAT = bootstrp (..., D, 'weights', WEIGHTS)' sets the resampling
+ weights. WEIGHTS must be a column vector with the same number of rows as
+ the data, D. If WEIGHTS is empty or not provided, the default is a vector
+ of length N with uniform weighting 1/N.
+
+ 'BOOTSTAT = bootstrp (..., D1, ... DN, 'weights', WEIGHTS)' as above if
+ MATCH is true. If MATCH is false, a 1-by-N cell array of column vectors
+ can be provided to specify independent resampling weights for D1 to DN.
+
+ 'BOOTSTAT = bootstrp (..., 'loo', LOO)' sets the simulation 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.
+
+ 'BOOTSTAT = bootstrp (..., 'seed', SEED)' initialises the Mersenne Twister
+ random number generator using an integer SEED value so that bootci results
+ are reproducible.
+
+ '[BOOTSTAT, BOOTSAM] = bootstrp (...)' also returns indices used for
+ bootstrap resampling. If MATCH is true or only one data argument is
+ provided, BOOTSAM is a matrix. If multiple data arguments are provided
+ and MATCH is false, BOOTSAM is returned in a 1-by-N cell array of
+ matrices, where each cell corresponds to the respective data argument
+ D1 to DN.
Bibliography:
[1] Efron, and Tibshirani (1993) An Introduction to the
@@ -69,8 +104,11 @@ bootstrp
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.
- bootstrp (version 2023.06.20)
+ bootstrp (version 2024.04.23)
Author: Andrew Charles Penn
https://www.researchgate.net/profile/Andrew_Penn/
@@ -99,64 +137,169 @@
0 33 28 34 4 32 24 47 41 24 26 30 41]';
% Compute 50 bootstrap statistics for the mean and calculate the bootstrap
- % standard arror
- bootstat = bootstrp (50, @mean, data)
+ % standard error of the mean
+ bootstat = bootstrp (50, @mean, data, 'seed', 1);
+ % Or equivalently
+ bootstat = bootstrp (50, @mean, data, 'seed', 1, 'loo', false);
+ std (bootstat)
+Produces the following output
+ans = 2.7156
+
+
+ Balanced bootstrap resampling.
+ Bootstrap resampling.
Performs single or double bootstrap (or bootknife) resampling and calculates confidence intervals.
diff --git a/docs/index.html b/docs/index.html
index 6f94d84d..bb3104fb 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -3,7 +3,7 @@