abcnon               package:bootstrap               R Documentation

_N_o_n_p_a_r_a_m_e_t_r_i_c _A_B_C _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:

     abcnon(x, tt, epsilon=0.001, 
            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: the data. Must be either a vector, or a matrix whose rows are
          the observations

      tt: function defining the parameter in the resampling form
          `tt(p,x)', where `p' is the vector of proportions and `x' is
          the data

 epsilon: optional argument specifying step size for finite difference
          calculations

   alpha: optional argument specifying confidence levels desired

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

     list with following components 

  limits: The estimated confidence points, from the ABC and standard
          normal methods

   stats: list consisting of `t0'=observed value of `tt',
          `sighat'=infinitesimal jackknife estimate  of standard error
          of `tt', `bhat'=estimated bias

constants: list consisting of `a'=acceleration constant, `z0'=bias
          adjustment, `cq'=curvature component

  tt.inf: approximate influence components of `tt'

      pp: matrix whose rows are the resampling points in the least
          favourable family. The abc confidence points are the function
          `tt' evaluated at these points

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

     Efron, B, and DiCiccio, T. (1992) More accurate confidence
     intervals  in exponential families. Biometrika 79, pages 231-245.

     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:

     # compute abc intervals for the mean
     x <- rnorm(10)
     theta <- function(p,x) {sum(p*x)/sum(p)}
     results <- abcnon(x, theta)  
     # compute abc intervals for the correlation
     x <- matrix(rnorm(20),ncol=2)
     theta <- function(p, x)
     {
         x1m <- sum(p * x[, 1])/sum(p)
         x2m <- sum(p * x[, 2])/sum(p)
         num <- sum(p * (x[, 1] - x1m) * (x[, 2] - x2m))
         den <- sqrt(sum(p * (x[, 2] - x1m)^2) *
                   sum(p * (x[, 2] - x1m)^2))
         return(num/den)
     }
     results <- abcnon(x, theta)   

