bootstrap             package:bootstrap             R Documentation

_N_o_n-_P_a_r_a_m_e_t_r_i_c _B_o_o_t_s_t_r_a_p_p_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     See Efron and Tibshirani (1993) for details on this function.

_U_s_a_g_e:

     bootstrap(x,nboot,theta,..., func=NULL)

_A_r_g_u_m_e_n_t_s:

       x: a vector containing the data. To bootstrap more complex data
          structures (e.g. bivariate data) see the last example below.

   nboot: The number of bootstrap samples desired.

   theta: function to be bootstrapped. Takes `x' as an argument, and
          may take additional arguments (see below and last example).

     ...: any additional arguments to be passed to `theta'

    func: (optional) argument specifying the functional the
          distribution of thetahat that is desired.  If func is
          specified, the jackknife after-bootstrap estimate of its
          standard error is also returned. See example below.

_V_a_l_u_e:

     list with the following components: 

thetastar: the `nboot' bootstrap values of `theta'

func.thetastar: the functional `func' of the bootstrap distribution of
          thetastar, if `func' was specified

jack.boot.val: the jackknife-after-bootstrap values for `func', if
          `func' was specified

jack.boot.se: the jackknife-after-bootstrap standard error estimate of
          `func', if `func' was specified

_R_e_f_e_r_e_n_c_e_s:

     Efron, B. and   Tibshirani, R. (1986).  The bootstrap method for
     standard errors, confidence intervals, and other measures of  
     statistical accuracy. Statistical Science, Vol 1., No. 1, pp 1-35.

     Efron, B. (1992) Jackknife-after-bootstrap standard errors and
     influence functions. J. Roy. Stat. Soc. B, vol 54, pages 83-127

     Efron, B. and Tibshirani, R. (1993) An Introduction to the
     Bootstrap. Chapman and Hall, New York, London.

_E_x_a_m_p_l_e_s:

     # 100 bootstraps of the sample mean 
     # (this is for illustration;  since "mean" is  a 
     # built in function, bootstrap(x,100,mean) would be simpler!)
     x <- rnorm(20)                
     theta <- function(x){mean(x)} 

     results <- bootstrap(x,100,theta)     

     # as above, but also estimate the 95th percentile   
     # of the bootstrap dist'n of the mean, and         
     # its jackknife-after-bootstrap  standard error    

     perc95 <- function(x){quantile(x, .95)}


     results <-  bootstrap(x,100,theta, func=perc95)                                   

     # To bootstrap functions of more complex data structures, 
     # write theta so that its argument x
     #  is the set of observation numbers  
     #  and simply  pass as data to bootstrap the vector 1,2,..n. 
     # For example, to bootstrap
     # the correlation coefficient from a set of 15 data pairs:
     xdata <- matrix(rnorm(30),ncol=2)
     n <- 15
     theta <- function(x,xdata){ cor(xdata[x,1],xdata[x,2]) }
     results <- bootstrap(1:n,20,theta,xdata)

