the contour is oriented clock-wise. For Cov ( η, ζ ) , we have so that by Cauchy’s theorem. For Var ( ζ ) , we have so that by Cauchy’s theorem. □ Lemma A3 and formulae (25) and (26) imply the convergence of finite dimensional- distributions of the random fields ln L ( h ; λ ) and ln L ( h ; µ ) to the Gaussian distri- 36 Var ( ζ ) = − 4 π i 4 π 2 ∮ ∮ ( z ( m$_{2}$ )) 2 m 2 ( c − 1 m$_{2}$ ) d m$_{2}$ = − 4 π i 4 π 2 ∮ ∮ ( − 1 m$_{2}$ + c 1+ m$_{2}$ ) 2 ( c − 1 m$_{2}$ ) m 2 d m$_{2}$ = 2 c ( 2 + 5 c + 2 c $^{2}$) ∮ z ( m$_{1}$ ) 2 ( m$_{1}$ − m$_{2}$ ) $_{2}$d m$_{1}$ = ∮ ( − 1 m$_{1}$ + c 1+ m$_{1}$ ) 2 ( m$_{1}$ − m$_{2}$ ) 2 d m$_{1}$ = 4 π i m 2 ( c − 1 m$_{2}$ ) Cov ( η, ζ ) = − 2 π i 4 π 2 ∮ ∮ ( z ( m$_{2}$ )) 2 m 2 d m$_{2}$ = − 2 π i 4 π 2 ( − 1 m$_{2}$ + c 1 + m$_{2}$ ) 2 1 m 2 d m$_{2}$ = 2 c (1 + c ) ∮ z ( m$_{1}$ ) ( m$_{1}$ − m$_{2}$ ) $_{2}$d m$_{1}$ = ∮ ( − 1 m$_{1}$ + c 1+ m$_{1}$ ) ( m$_{1}$ − m$_{2}$ ) 2 d m$_{1}$ = 2 π i m 2