Bootstrap confidence interval
ci = bootci(nboot,bootfun,...)
ci = bootci(nboot,{bootfun,...},'alpha',alpha)
ci = bootci(nboot,{bootfun,...},...,'type',type)
ci = bootci(nboot,{bootfun,...},...,'type','student','nbootstd',nbootstd)
ci = bootci(nboot,{bootfun,...},...,'type','student','stderr',stderr)
ci = bootci(nboot,{bootfun,...},...,'Weights',weights)
ci = bootci(nboot,{bootfun,...},...,'Options',options)
[ci,bootstat] = bootci(...)
ci = bootci(nboot,bootfun,...) computes
the 95% bootstrap confidence interval of the statistic computed by
the function bootfun. nboot is
a positive integer indicating the number of bootstrap samples used
in the computation. bootfun is a function handle
specified with @. The third and later input arguments
to bootci are data (scalars, column vectors, or
matrices) that are used to create inputs to bootfun. bootci creates
each bootstrap sample by sampling with replacement from the rows of
the non-scalar data arguments (these must have the same number of
rows). Scalar data are passed to bootfun unchanged.
If bootfun returns a scalar, ci is
a vector containing the lower and upper bounds of the confidence interval.
If bootfun returns a vector of length m, ci is
an array of size 2-by-m, where ci(1,:) are
lower bounds and ci(2,:) are upper bounds. If bootfun returns
an array of size m-by-n-by-p-by-..., ci is
an array of size 2-by-m-by-n-by-p-by-...,
where ci(1,:,:,:,...) is an array of lower bounds
and ci(2,:,:,:,...) is an array of upper bounds.
ci = bootci(nboot,{bootfun,...},'alpha',alpha) computes
the 100*(1-alpha) bootstrap confidence interval
of the statistic defined by the function bootfun. bootfun and
the data that bootci passes to it are contained
in a single cell array. alpha is a scalar between 0 and 1.
The default value of alpha is 0.05.
ci = bootci(nboot,{bootfun,...},...,'type', computes
the bootstrap confidence interval of the statistic defined by the
function type)bootfun. type
'norm' or 'normal' —
Normal approximated interval with bootstrapped bias and standard error.
'per' or 'percentile' —
Basic percentile method.
'cper' or 'corrected percentile' —
Bias corrected percentile method.
'bca' — Bias corrected and
accelerated percentile method. This is the default.
'stud' or 'student' —
Studentized confidence interval.
ci = bootci(nboot,{bootfun,...},...,'type','student','nbootstd',nbootstd) computes
the studentized bootstrap confidence interval of the statistic defined
by the function bootfun. The standard error of
the bootstrap statistics is estimated using bootstrap, with nbootstd bootstrap
data samples. nbootstd is a positive integer value.
The default value of nbootstd is 100.
ci = bootci(nboot,{bootfun,...},...,'type','student','stderr',stderr) computes
the studentized bootstrap confidence interval of statistics defined
by the function bootfun. The standard error of
the bootstrap statistics is evaluated by the function stderr. stderr is
a function handle. stderr takes the same arguments
as bootfun and returns the standard error of the
statistic computed by bootfun.
ci = bootci(nboot,{bootfun,...},...,'Weights',weights) specifies
observation weights. weights must be a vector of
non-negative numbers with at least one positive element. The number
of elements in weights must be equal to the number
of rows in non-scalar input arguments to bootfun.
To obtain one bootstrap replicate, bootstrp samples N out
of N with replacement using these weights as multinomial
sampling probabilities.
ci = bootci(nboot,{bootfun,...},...,'Options',options) specifies
options that govern the computation of bootstrap iterations. One option
requests that bootci perform bootstrap iterations
using multiple processors, if the Parallel Computing Toolbox™ is
available. Two options specify the random number streams to be used
in bootstrap resampling. This argument is a struct that you can create
with a call to statset. You can
retrieve values of the individual fields with a call to statget. Applicable statset parameters
are:
'UseParallel' — If true and
if a parpool of the Parallel Computing Toolbox is
open, compute bootstrap iterations in parallel. If the Parallel Computing Toolbox is
not installed, or a parpool is not open, computation
occurs in serial mode. Default is false, or serial
computation.
UseSubstreams — Set to true to
compute in parallel in a reproducible fashion. Default is false.
To compute reproducibly, set Streams to a type
allowing substreams: 'mlfg6331_64' or 'mrg32k3a'.
Streams — A RandStream object or cell array of such
objects. If you do not specify Streams, bootci uses
the default stream or streams. If you choose to specify Streams,
use a single object except in the case
UseParallel is true
UseSubstreams is false
In that case, use a cell array the same size as the Parallel pool.
[ci,bootstat] = bootci(...) also returns
the bootstrapped statistic computed for each of the nboot bootstrap
replicate samples. Each row of bootstat contains
the results of applying bootfun to one bootstrap
sample. If bootfun returns a matrix or array, then
this output is converted to a row vector for storage in bootstat.
Compute the confidence interval for the capability index in statistical process control:
y = normrnd(1,1,30,1); % Simulated process data
LSL = -3; USL = 3; % Process specifications
capable = @(x)(USL-LSL)./(6* std(x)); % Process capability
ci = bootci(2000,capable,y) % BCa confidence interval
ci =
0.8122
1.2657
sci = bootci(2000,{capable,y},'type','student') % Studentized ci
sci =
0.7739
1.2707