

jackknife(bootstrap)                         R Documentation

_J_a_c_k_k_n_i_f_e _E_s_t_i_m_a_t_i_o_n

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

     jackknife(x, theta, ...)

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

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

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

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

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

     list with the following components

 jack.se: The jackknife estimate of standard error of
          `theta'.  The leave-one out jackknife is used.

jack.bias: The jackknife estimate of bias of `theta'.  The
          leave-one out jackknife is used.

jack.values: The n leave-one-out values of `theta', where n
          is the number of observations.  That is, `theta'
          applied to `x' with the 1st observation deleted,
          `theta' applied to `x' with the 2nd observation
          deleted, etc.

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

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

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

     results <- jackknife(x,theta)

     # To jackknife 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 jackknife the vector 1,2,..n.
     # For example, to jackknife
     # 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 <- jackknife(1:n,theta,xdata)

