BIOS 280
                           Survival Analysis
                               Homework 2
                               2/1/1996



Read:
  K&P, chapters 4, 5.
  Cox (1972) JRSS, p 187.
  Cox (1975) Biometrika (Partial Likelihood) p 269.


1.
Suppose T_1, ..., T_n are i.i.d from a Weibull distribution with
parameters \lambda=1, \kappa=2; H(t) = (\lambda t)^\kappa.
We wish to estimate S(0.8325546112), which happens to be 0.5.
Note: There is no censoring.

Consider two estimators:
(i)  One based on the empirical distribution function.
(ii) One based on fitting an exponential model, which is the wrong model.
Large sample theory tells us that the second estimator is not consistent.

Tabulate the root mean square error (RMSE) for each estimator for sample
sizes n=1, 5, 10, 15, 20, 25.  Use simulation approximation if exact
quantities are difficult to compute.
Present a table showing bias, variance and RMSE for each n.
Comment.



2. K&P, #15 (page 243).