bcanon               package: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

_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:

     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 constructing 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)

