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 and ν > 0 is a parameter. a) Show that the score function...

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 and ν > 0 is a parameter.

a) Show that the score function takes the form
  where τ is the upper time limit of the study,
 and a dot means summation over i = 1,2,...,n.

b) Show that, when evaluated at the true value of the parameter, the expected value of the score is zero and its variance equals

c) Derive the observed information i(ν) = −U ′ (ν) and show that its expected value, when evaluated at the true value of the parameter, equals E(R(τ)/ν).

Chapter 6