| Asymptotical expansions for distribution function of one kind of extended Pickands-type estimator.and the joint limiting distribution of location and height of the second maxima for nonstationary,weakly dependent normal sequences had been considered in this paper respectively.Firstly,the Pickands-type estimator had been proposed by Pickands in 1975.In 1997,Pengt proposed the extended Pickands-type estimatorwhere ki = ki(n),i = 1,2,3,4 satisfyX1,X2,......, Xn is an i.i.d. sequence of random variables with common distribution F(x),X1,n≤ X2,n≤......≤ Xn,n are the ascending order statistics ofX1, X2,……,Xn.Under some weak conditions, the asymptotic expansions for distribution function of one kind of extended Pickands-type estimator has been given under the conditions c >1/d.Secondly,under the conditionthe joint asymptotic distribution of the location and the height of the second maximum for a kind of nonstationary,weakly dependent Gaussian sequences {ηi} in (3.1) has been given.
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