R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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>  # slr2.r
>  # first probe on SimStudy problem 2
>  # normality of L1 regression
>  #
>   y <- c(4.5,5.5,6.5,8,10,12)
>   x <- (1:6)
>  #
>   g <- function(b) {
+          res <- y - b*x
+          med <- median(res)
+          g <- sum(abs(res-med)) }
>  # 
>  # simple linear regression
>   slr <- function(y,x) {
+     xb <- mean(x)
+     yb <- mean(y)
+     sxx <- sum((x-xb)*(x-xb))
+     b1 <- sum((x-xb)*(y-yb))/sxx
+     b0 <- yb - b1*xb
+     sse <- sum((y-b0-b1*x)*(y-b0-b1*x))
+     slr <- c(b0,b1,sqrt(sse/((length(x)-2)*sxx)))   }
>  #
>     rslt <- slr(y,x)
>     rslt
[1] 2.5000000 1.5000000 0.1195229
>     int <- c(rslt[2]-4*rslt[3],rslt[2]+4*rslt[3]) # +/- 4 se's
>     int
[1] 1.021909 1.978091
>  # use optimize on smoother function 
>     this <- optimize(g,int)
>     this
$minimum
[1] 1.5

$objective
[1] 2

>  # different approach
>    c2 <- .1
>    h <- function(u){sqrt(c2+u*u)}
>    hp <- function(u){u/sqrt(c2+u*u)}
>    hpp <- function(u){c2/((c2+u*u)*sqrt(c2+u*u))}
>     b <- c(1,1)
>    for ( i in(1:5) ) {        # iterate on i
+     e <- y - b[1] - x*b[2]
+     print(e)
+     print(sapply(e,h))
+     print(sum(sapply(e,h)))
+     hpatb <- sapply(e,hp)
+     hppatb <- sapply(e,hpp)
+     print(hpatb)
+     print(hppatb)
+     grad <- -c(sum(hpatb),sum(x*hpatb))
+     print(grad)
+     hess <- matrix(c(sum(hppatb),sum(x*hppatb),sum(x*hppatb),
+                   sum(x*x*hppatb)),2,2)
+     print(hess)
+     b <- b - solve(hess,grad)
+     print(c(i,b)) }
[1] 2.5 2.5 2.5 3.0 4.0 5.0
[1] 2.519921 2.519921 2.519921 3.016621 4.012481 5.009990
[1] 19.59885
[1] 0.9920947 0.9920947 0.9920947 0.9944903 0.9968896 0.9980060
[1] 0.0062494157 0.0062494157 0.0062494157 0.0036428217 0.0015479652
[6] 0.0007952239
[1]  -5.96567 -20.90301
           [,1]       [,2]
[1,] 0.02473426 0.06457895
[2,] 0.06457895 0.21310416
[1]   1.00000 -70.40687 120.72734
[1]  -45.82047 -165.54781 -285.27516 -404.50250 -523.22984 -641.95718
[1]  45.82156 165.54811 285.27533 404.50262 523.22994 641.95726
[1] 2066.335
[1] -0.9999762 -0.9999982 -0.9999994 -0.9999997 -0.9999998 -0.9999999
[1] 1.039418e-06 2.204080e-08 4.307322e-09 1.510901e-09 6.981074e-10
[6] 3.779912e-10
[1]  5.999973 20.999968
             [,1]         [,2]
[1,] 1.068353e-06 1.108224e-06
[2,] 1.108224e-06 1.221582e-06
[1]          2  207266770 -205223933
[1]   -2042833  203181101  408405036  613628970  818852906 1024076841
[1]    2042833  203181101  408405036  613628970  818852906 1024076841
[1] 3070187687
[1] -1  1  1  1  1  1
[1] 1.173010e-20 1.192203e-26 1.468002e-27 4.327952e-28 1.821303e-28
[6] 9.311129e-29
[1]  -4 -19
             [,1]         [,2]
[1,] 1.173011e-20 1.173013e-20
[2,] 1.173013e-20 1.173017e-20
[1]  3.000000e+00 -5.569785e+26  5.569780e+26
[1]  4.828466e+20 -5.569775e+26 -1.113956e+27 -1.670934e+27 -2.227912e+27
[6] -2.784890e+27
[1] 4.828466e+20 5.569775e+26 1.113956e+27 1.670934e+27 2.227912e+27
[6] 2.784890e+27
[1] 8.354668e+27
[1]  1 -1 -1 -1 -1 -1
[1] 8.883263e-64 5.787446e-82 7.234298e-83 2.143495e-83 9.042867e-84
[6] 4.629947e-84
[1]  4 19
             [,1]         [,2]
[1,] 8.883263e-64 8.883263e-64
[2,] 8.883263e-64 8.883263e-64