L3 Lk fak

Denote the solution to this working likelihood by 3 = ( fa1, fa2, • • • , faK). WLW show that when Xk(t\Z) = Xk(t)exp(faZ), 3 is consistent and asymptotically

normal as n —> oo; that is, 3 ¡3 and ^(¡3 - ¡3) N(0, S), where S = VD1VVD1, V is a K-dimensional matrix obtained from the working likelihood (see Appendix 1), and Vd is the diagonal matrix with the same diagonal elements as V. WLW also provide a consistent sandwich estimate of S, which we denote by S.

WLW propose a directional and omnibus test of Ho, which we denote by Q2 and Q3, respectively. Specifically, n(c23)2 _ n(1'S-13)2

c'2Sc2 1'E-11 ' where c2 = and 1 is a vector with elements all equal to 1, and

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