>  # 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)
[1] "t1,t2,sse"
[1] 46.26346  0.10000 87.49828
>    sse(1)
[1] "t1,t2,sse"
[1] 16.64283  1.00000 42.85488
>    sse(5)
[1] "t1,t2,sse"
[1]  14.85742   5.00000 105.90782
>    sse(10)
[1] "t1,t2,sse"
[1]  14.83350  10.00000 107.20453
>  # minimize error sum of squares
>    that2 <- optimize(f=sse,lower=.1,upper=5) 
[1] "t1,t2,sse"
[1] 15.376096  1.971633 80.639967
[1] "t1,t2,sse"
[1] 14.993260  3.128367 98.750177
[1] "t1,t2,sse"
[1] 16.099940  1.256733 55.200735
[1] "t1,t2,sse"
[1] 17.2634313  0.8149004 33.9910427
[1] "t1,t2,sse"
[1] 19.0324039  0.5418327 26.0078259
[1] "t1,t2,sse"
[1] 21.5716334  0.3730676 31.0740041
[1] "t1,t2,sse"
[1] 18.7704232  0.5693695 26.2033106
[1] "t1,t2,sse"
[1] 19.0831309  0.5368292 25.9953196
[1] "t1,t2,sse"
[1] 19.1488920  0.5304894 25.9903235
[1] "t1,t2,sse"
[1] 19.1430332  0.5310477 25.9902676
[1] "t1,t2,sse"
[1] 19.1425429  0.5310945 25.9902673
[1] "t1,t2,sse"
[1] 19.1421164  0.5311352 25.9902676
[1] "t1,t2,sse"
[1] 19.1425429  0.5310945 25.9902673
>  # print it out
>    print("min sse")
[1] "min sse"
>    print(that2)
$minimum
[1] 0.5310945

$objective
[1] 25.99027

>  # done
>    rm(list=ls())
>  q()