lines.saddle.distn           package:boot           R Documentation

Add a Saddlepoint Approximation to a Plot

Description:

     This function adds a line corresponding to a saddlepoint density
     or  distribution function approximation to the current plot.

Usage:

     ## S3 method for class 'saddle.distn':
     lines(x, dens = TRUE, h = function(u) u, J = function(u) 1, 
          npts = 50, lty = 1, ...)

Arguments:

       x: An object of class '"saddle.distn"'  (see
          'saddle.distn.object' representing a saddlepoint
          approximation to a distribution. 

    dens: A logical variable indicating whether the saddlepoint density
          ('TRUE'; the default) or the saddlepoint distribution
          function ('FALSE') should be plotted. 

       h: Any transformation of the variable that is required.  Its
          first argument must be the value at which the approximation
          is being performed and the function must be vectorized. 

       J: When 'dens=TRUE' this function specifies the Jacobian for any
          transformation that may be necessary.  The first argument of
          'J' must the value at which the approximation is being
          performed and the function must be vectorized. If 'h' is
          supplied 'J' must also be supplied and both must have the
          same argument list. 

    npts: The number of points to be used for the plot.  These points
          will be evenly spaced over the range of points used in
          finding the saddlepoint approximation. 

     lty: The line type to be used. 

     ...: Any additional arguments to 'h' and 'J'. 

Details:

     The function uses 'smooth.spline' to produce the saddlepoint
     curve.  When 'dens=TRUE' the spline is on the log scale and when
     'dens=FALSE' it is on the probit scale.

Value:

     'sad.d' is returned invisibly.

Side Effects:

     A line is added to the current plot.

References:

     Davison, A.C. and Hinkley, D.V. (1997)  _Bootstrap Methods and
     Their Application_. Cambridge University Press.

See Also:

     'saddle.distn'

Examples:

     # In this example we show how a plot such as that in Figure 9.9 of
     # Davison and Hinkley (1997) may be produced.  Note the large number of
     # bootstrap replicates required in this example.
     expdata <- rexp(12)
     vfun <- function(d, i) 
     {    n <- length(d)
          (n-1)/n*var(d[i])
     }
     exp.boot <- boot(expdata,vfun, R = 9999)
     exp.L <- (expdata-mean(expdata))^2 - exp.boot$t0
     exp.tL <- linear.approx(exp.boot, L = exp.L)
     hist(exp.tL, nclass = 50, prob = TRUE)
     exp.t0 <- c(0,sqrt(var(exp.boot$t)))
     exp.sp <- saddle.distn(A = exp.L/12,wdist = "m", t0 = exp.t0)

     # The saddlepoint approximation in this case is to the density of
     # t-t0 and so t0 must be added for the plot.
     lines(exp.sp,h = function(u,t0) u+t0, J = function(u,t0) 1,
           t0 = exp.boot$t0)

