Stat 550    HW 2    1-29-2011    D. Scott    Due 2-3


Problems from Chapter 2


ToDo:  
1.  2
2.  6 (1st part)
3.  7
4. 10
5.  Generate a normal sample in R as follow:
    	 set.seed(234); x = rnorm(100)
    Using the L2E parametric criterion, plot
    contours of the criterion as a function
    of mu and sigma;  find the minimizer and
    compare to the MLE values.

    Repeat using this sample:
    	   set.seed(245); x = c(rnorm(100), rnorm(25,5))


Hints for problem 5 (and a useful identity):

       [In class, I did not compute the ISE correctly.
        ISE = integral   [fhat(x)-f(x)]^2 .   Thus
        there are 3 integrals, not just the one I computed.]

       Compute the ISE in closed form as a function of the
       sample mean.  Then take the expected value knowing
       the sampling density of the sample mean.

       Let phi(x;m,v) be a normal density with mean m and variance v.

       Then:

         integral over the entire real line of

           phi(x;m1,v1) times  phi(x;m2,v2)  =   phi(x=0; m1-m2, v1+v2 )