Assume that the counting processes N i (t), i = 1,2,...,n, have intensity processes of the form  where the Y i (t) are at risk indicators. We introduce a) Show that the maximum likelihood estimator is...

Assume that the counting processes N_i(t), i = 1,2,...,n, have intensity processes of the form

 where the Y_i(t) are at risk indicators. We introduce

a) Show that the maximum likelihood estimator is

b) Show that
  is approximately normally distributed around the true value of β with a variance that may be estimated by 1/N(τ)

c) Use the result in question (b) to derive an approximate 95% confidence interval for ν = logβ.