_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 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). 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_s: list with the following components: thetastar: the nboot bootstrap values of theta func.thetastar: the functional func of the bootstrap distri- bution 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)