Jackknife sampling

`jackstat = jackknife(jackfun,X)`

jackstat = jackknife(jackfun,X,Y,...)

jackstat = jackknife(jackfun,...,'Options',option)

`jackstat = jackknife(jackfun,X)`

draws
jackknife data samples from the `n`

-by-`p`

data
array `X`

, computes statistics on each sample using
the function `jackfun`

, and returns the results in
the matrix `jackstat`

. `jackknife`

regards
each row of `X`

as one data sample, so there are `n`

data
samples. Each of the `n`

rows of `jackstat`

contains
the results of applying `jackfun`

to one jackknife
sample. `jackfun`

is a function handle specified
with `@`

. Row `i`

of `jackstat`

contains
the results for the sample consisting of `X`

with
the `i`

th row omitted:

s = x; s(i,:) = []; jackstat(i,:) = jackfun(s);

`jackfun`

returns
a matrix or array, then this output is converted to a row vector for
storage in `jackstat`

. If `X`

is
a row vector, it is converted to a column vector.`jackstat = jackknife(jackfun,X,Y,...)`

accepts
additional arguments to be supplied as inputs to `jackfun`

.
They may be scalars, column vectors, or matrices. `jackknife`

creates
each jackknife 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 `jackfun`

unchanged.
Non-scalar arguments must have the same number of rows, and each
jackknife sample omits the same row from these arguments.

`jackstat = jackknife(jackfun,...,'Options',option)`

provides
an option to perform jackknife iterations in parallel, if the Parallel
Computing Toolbox™ is
available. Set `'Options'`

as a structure you create
with `statset`

. `jackknife`

uses
the following field in the structure:

`'UseParallel'` | If |

Estimate the bias of the MLE variance estimator of random samples taken from the vector
`y`

using `jackknife`

. The bias has a known formula
in this problem, so you can compare the `jackknife`

value to this
formula.

sigma = 5; y = normrnd(0,sigma,100,1); m = jackknife(@var,y,1); n = length(y); bias = -sigma^2/n % known bias formula jbias = (n-1)*(mean(m)-var(y,1)) % jackknife bias estimate bias = -0.2500 jbias = -0.3378