jackknife             package:bootstrap             R Documentation

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

_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:

     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 argument, 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)

