TITLE(bootpred @@ bootstrap estimates of prediction error )
USAGE(
bootpred(x,y,nboot,theta.fit,theta.predict,err.meas,...)
)
ARGUMENTS(
ARG(x@@
a matrix containing the predictor (regressor) values. Each row
corresponds to an observation. )
ARG(y@@
a vector containing the response values)
ARG(nboot@@
the number of bootstrap replications)
ARG(theta.fit@@
function to be cross-validated. Takes x and y as an argument.
See example below.)
ARG(theta.predict@@
function producing predicted values for theta.fit.
Arguments are a matrix x of predictors and fit object produced by theta.fit.
See example below.)
ARG(err.meas@@
function specifying error measure for a single response y and prediction yhat
 - see examples below)
ARG(...@@
any additional arguments to be passed to theta.fit)
)
VALUES(
list with the following components
ARG(app.err@@
the apparent error rate- that is, the mean value of err.meas when theta.fit
is applied to x and y, and then used to predict y.)
ARG(optim@@
the bootstrap estimate of optimism in app.err. A useful
estimate of prediction error is app.err+optim)
ARG(err.632@@
the ".632" bootstrap estimate of prediction error.)
REFERENCES(
Efron, B. (1983). Estimating the error rate of a prediction rule: improvements
on cross-validation. J. Amer. Stat. Assoc, vol 78. pages 316-31.
PARA
Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap.
Chapman and Hall, New York, London.)
)
EXAMPLES(
# bootstrap prediction error estimation in least squares
#  regression
x <- rnorm(85)  
y <- 2*x +.5*rnorm(85)                      
theta.fit <- function(x,y)\{lsfit(x,y)\}
theta.predict <- function(fit,x)\{
               cbind(1,x)%*%fit\$coef         
               \}    
sq.err_function(y,yhat) \{ (y-yhat)^2\}                   
results <- bootpred(x,y,20,theta.fit,theta.predict,
     err.meas=sq.err)  
                                      
# for a classification problem, a standard choice 
# for err.meas would simply count up the
#  classification errors:
miss.clas <- function(y,yhat)\{ 1*(yhat!=y)\}
# with this specification,  bootpred estimates 
#  misclassification rate
)

