empinf {boot}  R Documentation 
This function calculates the empirical influence values for a statistic applied to a data set. It allows four types of calculation, namely the infinitesimal jackknife (using numerical differentiation), the usual jackknife estimates, the "positive" jackknife estimates and a method which estimates the empirical influence values using regression of bootstrap replicates of the statistic. All methods can be used with one or more samples.
empinf(boot.out=NULL, data=NULL, statistic=NULL, type=NULL, stype="w", index=1, t=NULL, strata=rep(1, n), eps=0.001, ...)
boot.out 
A bootstrap object created by the function boot . If type is "reg" then
this argument is required. For any of the other types it is
an optional argument. If it is included when optional then the values of
data , statistic , stype , and strata are taken from the components of
boot.out and any values passed to empinf directly are ignored.

data 
A vector, matrix or data frame containing
the data for which empirical influence values are required. It is a required
argument if boot.out is not supplied. If boot.out is supplied then data
is set to boot.out$data and any value supplied is ignored.

statistic 
The statistic for which empirical influence values are required. It must be
a function of at least two arguments, the data set and
a vector of weights, frequencies or indices. The nature of the second
argument is given by the value of stype . Any other arguments that it
takes must be supplied to empinf and will be passed to statistic unchanged.
This is a required argument if boot.out is not supplied, otherwise its value
is taken from boot.out and any value supplied here will be ignored.

type 
The calculation type to be used for the empirical influence values.
Possible values of type are "inf" (infinitesimal jackknife), "jack"
(usual jackknife), "pos" (positive jackknife), and "reg" (regression
estimation). The default value depends on the other arguments. If t is supplied then the default value of type is "reg" and boot.out
should be present so that its frequency array can be found. It t is not
supplied then if stype is "w" , the default value of type is "inf" ; otherwise, if boot.out is present the default is "reg" . If
none of these conditions apply then the default is "jack" .
Note that it is an error for type to be
"reg" if boot.out is missing or to be "inf" if stype is not "w" .

stype 
A character variable giving the nature of the second argument to statistic .
It can take on three values: "w" (weights), "f" (frequencies), or "i"
(indices). If boot.out is supplied the value of stype is set to
boot.out$stype and any value supplied here is ignored. Otherwise it is an
optional argument which defaults to "w" . If type is "inf" then stype
MUST be "w" .

index 
An integer giving the position of the variable of interest in the output of
statistic .

t 
A vector of length boot.out$R which gives the bootstrap replicates of the
statistic of interest. t is used only when type is reg and it defaults
to boot.out$t[,index] .

strata 
An integer vector or a factor specifying the strata for multisample problems.
If boot.out is supplied the value of strata is set to boot.out$strata .
Otherwise it is an optional argument which has default corresponding to the
single sample situation.

eps 
This argument is used only if type is "inf" . In that case the value of
epsilon to be used for numerical differentiation will be eps divided by
the number of observations in data .

... 
Any other arguments that statistic takes. They will be passed unchanged to
statistic every time that it is called.

If type
is "inf"
then numerical differentiation is used to approximate the
empirical influence values. This makes sense only for statistics which
are written in weighted form (i.e. stype
is "w"
). If type
is "jack"
then the
usual leaveoneout jackknife estimates of the empirical influence are
returned. If type
is "pos"
then the positive (includeonetwice) jackknife
values are used. If type
is "reg"
then a bootstrap object must be supplied.
The regression method then works by regressing the bootstrap replicates of
statistic
on the frequency array from which they were derived. The
bootstrap frequency array is obtained through a call to boot.array
. Further
details of the methods are given in Section 2.7 of Davison and Hinkley (1997).
Empirical influence values are often used frequently in nonparametric bootstrap
applications. For this reason many other functions call empinf
when they
are required. Some examples of their use are for nonparametric delta estimates
of variance, BCa intervals and finding linear approximations to statistics for
use as control variates. They are also used for antithetic bootstrap
resampling.
A vector of the empirical influence values of statistic
applied to data
.
The values will be in the same order as the observations in data.
All arguments to empinf
must be passed using the name=value
convention. If
this is not followed then unpredictable errors can occur.
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
Efron, B. (1982) The Jackknife, the Bootstrap and Other Resampling Plans. CBMSNSF Regional Conference Series in Applied Mathematics, 38, SIAM.
Fernholtz, L.T. (1983) von Mises Calculus for Statistical Functionals. Lecture Notes in Statistics, 19, SpringerVerlag.
boot
, boot.array
, boot.ci
, control
, jack.after.boot
, linear.approx
, var.linear
# The empirical influence values for the ratio of means in # the city data. ratio < function(d, w) sum(d$x *w)/sum(d$u*w) empinf(data=city,statistic=ratio) city.boot < boot(city,ratio,499,stype="w") empinf(boot.out=city.boot,type="reg") # A statistic that may be of interest in the difference of means # problem is the tstatistic for testing equality of means. In # the bootstrap we get replicates of the difference of means and # the variance of that statistic and then want to use this output # to get the empirical influence values of the tstatistic. grav1 < gravity[as.numeric(gravity[,2])>=7,] grav.fun < function(dat, w) { strata < tapply(dat[, 2], as.numeric(dat[, 2])) d < dat[, 1] ns < tabulate(strata) w < w/tapply(w, strata, sum)[strata] mns < tapply(d * w, strata, sum) mn2 < tapply(d * d * w, strata, sum) s2hat < sum((mn2  mns^2)/ns) c(mns[2]mns[1],s2hat) } grav.boot < boot(grav1, grav.fun, R=499, stype="w", strata=grav1[,2]) # Since the statistic of interest is a function of the bootstrap # statistics, we must calculate the bootstrap replicates and pass # them to empinf using the t argument. grav.z < (grav.boot$t[,1]grav.boot$t0[1])/sqrt(grav.boot$t[,2]) empinf(boot.out=grav.boot,t=grav.z)