Second order asymptotic efficlency in terms of the asymptotic variance of seqrential estimation procedures in the presence of nrisance parameters

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In the presence of nuisance parameters, the Bhattacharyya type bound for the asymptotic variance of estimation procedures is obtained. It is shown that the modified maximum likelihood (ML) estimation procedures together with any stopping rule does not attain the bound. Further it is shown that the modified ML estimation procedure with the appropriate stopping rule is second order asymptotically efficient in some class of estimation procedures in the sense that it attains the lower bound for the asymptotic variance in the class.