Asymptotic Properties Of Extremal Estimators

Soppose X1,X2,…,Xn is an i.i.d random sequence with commom distribution func-tion F(x),andX1,n,X2,n,…,Xn,n is its order statistics.If there exist constants an>0 and bn? R and {Xn,n-bn)/an converges to the domain of attraction of G?(x),Pr((Xn,n-bn)/an?x)=Fn(anx+bn)? G,So F ? D(G?(x))and ? is called the extreme value index.In the first part,I propose an estimator based on record values:and prove its weak convergence and asymptotic normality.Finally,the estimator is ana-lyzed by random simulation with R software programming to verify its effectiveness.In the second part,? propose a kind of location invariant estimator c to estimate rainfall index:and prove its weak convergence and asymptotic normality.The optimal choice of k0 is also discussed.Finally,random simulation is conducted between the new estimator and the estimator proposed by de Haan through R software programming to compare the effectiveness of them.