Then, 2rp/p is asymptotically a chi-squared random variable with 

 degrees of freedom. 



2r 



Proof: 



rp = Y 



m=mp.+ l 



/N A t 



/N A t 



2rp 

 P 



Z 



m=mQ+l '■ 



/Np At/ 2 



/Np At/ 2 



By item 8, the terms squared in the sum are asymptotically independent, 

 zero mean, unit-variance normal random variables. Hence, the right-hand 

 side is asymptotically chi-squared with 2r degrees of freedom (Freund, 

 1971). 



102 



