abcpar               package:bootstrap               R Documentation

_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:

     abcpar(y, tt, S, etahat, mu, n=rep(1,length(x)),lambda=0.001, 
            alpha=c(0.025, 0.05, 0.1, 0.16))

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

       y: vector of data

      tt: function of expectation parameter `mu' defining the parameter
          of interest

       S: maximum likelihood estimate of the covariance matrix of `x'

  etahat: maximum likelihood estimate of the natural parameter eta

      mu: function giving expectation of `x' in terms of eta

       n: optional argument containing denominators for binomial
          (vector of length `length(x)')

  lambda: optional argument specifying step size for finite difference
          calculation

   alpha: optional argument specifying confidence levels desired

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

     list with the following components 

    call: the call to abcpar

  limits: The nominal confidence level, ABC point, quadratic ABC point,
          and standard normal point.

   stats: list consisting of  observed value of `tt', estimated
          standard error and estimated bias

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

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

     Efron, B, and DiCiccio, T. (1992) More accurate confidence
     intervals  in exponential families. Bimometrika 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:

     # binomial
     # x is a p-vector of successes, n is a p-vector of 
     #  number of trials

     S <- matrix(0,nrow=p,ncol=p)
     S[row(S)==col(S)] <- x*(1-x/n)
     mu <- function(eta,n){n/(1+exp(eta))}
     etahat <- log(x/(n-x))
     #suppose p=2 and we are interested in mu2-mu1
     tt <- function(mu){mu[2]-mu[1]}
     x <- c(2,4); n <- c(12,12)
     a <- abcpar(x, tt, S, etahat,n)

