# conclk.r                       September 2007
 #
 # concentrated likelihood problem, Example 9.6
 #
  x <- c(1,2,3,4,5,7)
  y <- c(8.3, 10.3, 19.0, 16.0, 15.6, 19.8)
 #                  construct error sum of squares function
  sse <- function(t2) {
    z <- 1 - exp(-t2*x)
    t1 <- crossprod(y,z)/crossprod(z,z) # regression through origin
    e <- y - t1*z                       # residuals
    s <- crossprod(e,e)                 # error sum of squares
    print("t1,t2,sse")
    print(c(t1,t2,s))
    sse <- as.real(s) }                 # make it a scalar
 # starting values?
   sse(.1)
   sse(1)
   sse(5)
   sse(10)
 # minimize error sum of squares
   that2 <- optimize(f=sse,lower=.1,upper=5) 
 # print it out
   print("min sse")
   print(that2)
 # done
   rm(list=ls())
 q()