

bcanon(bootstrap)                            R Documentation

_N_o_n_p_a_r_a_m_e_t_r_i_c _B_C_a _C_o_n_f_i_d_e_n_c_e _L_i_m_i_t_s

_U_s_a_g_e_:

     bcanon(x, nboot, theta, ...,
            alpha=c(0.025, 0.05, 0.1, 0.16, 0.84, 0.9, 0.95, 0.975))

_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: number of bootstrap replications

   theta: function defining the estimator used in construct-
          ing the confidence points

     ...: additional arguments for `theta'

   alpha: optional argument specifying confidence levels
          desired

_V_a_l_u_e_:

     list with the following components

confpoint: estimated bca confidence limits

      z0: estimated bias correction

     acc: estimated acceleration constant

       u: jackknife influence values

_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. (1987). Better bootstrap confidence intervals
     (with discussion).  J. Amer. Stat. Assoc. vol 82, pg
     171

     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_:

     #  bca limits for the  mean
     #  (this is for illustration;
     #   since "mean" is a built in function,
     #   bcanon(x,100,mean) would be simpler!)
     x <- rnorm(20)
     theta <- function(x){mean(x)}
     results <- bcanon(x,100,theta)

     # To obtain bca limits for 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 bcanon
     # the vector 1,2,..n.
     # For example, find bca limits for
     # 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 <- bcanon(1:n,100,theta,xdata)

