denoted thn is the solution to the system of equations that results from approximating the expectation with respect to using an average of iid copies of xn psn (th: ps(xi thn = thuspsn ( thn theorem -estimator the -estimator is asymptotically normal as ( thn th- ( - ba-)( where :- ps ( thand : ps( thps( th)is the covariance matrix th of ps( th thn is unique rootthat isproofwe give proof under the simplifying assumption that for any th and ethere exists such that kb thn thk implies that kpsn (th) firstwe argue that thn -ththat isp[kb thn thk from the multivariate extension of theorem we have that psn (th- psn (the ps( th thereforeusing the uniqueness of thn we can show that thn -thvia the boundh kb thn thk kpsn (th) kpsn (the psn (th) thn around thto secondwe take taylor expansion of each component of the vector psn ( obtainpsn ( thn psn (thjn (th )( thn th)where jn (this the jacobian of psn at thand th lies on the segment joining thn and thline rearrange the last equation and multiply both sides by - to obtain- - jn (th ( thn tha- psn (thby the central limit theoremn ps(thconverges in distribution to ( btherefored - - jn (th ( thn th- ( - ba-theorem (the weak law of large numbersapplied to the iid random matrices th ps(xi th)shows that jn (th- ps( thth moreoversince thn -thand jn is continuous in thwe have that jn (th -- thereforep by slutsky' theorem- - jn (th ( thn thn ( thn th- the result holds under far less stringent assumptions