The asymptotic normality of the extreme - value index of extended moment estimator 極值指數(shù)之推廣矩估計量的漸近正態(tài)性
It comes up with a new notion , d - solution , which is applied to the distance estimation , by virtue of hilbert space ; furthermore , the dissertation has gained a necessary condition which is identity of minimum mean - square value in linear function classes , so that d - solution extends minimum mean - square value within the domain of nonlinear function equation or equation system ; and , the dissertation studies in detail the classical moment estimation and maximal likelihood estimation on the parameters of ar ( p ) , a series of theorems in the estimation section shows the moment estimators are consistent on the ground of large samples jikewise , those distribution functions of the estimated parameters accord to maximum likelihood estimation converge gauss distribution if the white noise is gaussan 首先,借助hilbert空間理論,提出了距離估計的d -解,給出了d -解的必要條件,這個條件在線性函數(shù)類里即是極小二乘估計法, d -解的必要條件滿足的方程實質(zhì)上將極小二乘估計法推廣到多函數(shù)及非線性函數(shù)類。再而,詳細(xì)地研究了多元弱平穩(wěn)序列自回歸模型ar ( p )的參數(shù)經(jīng)典的矩的替代估計和極大似然估計,獲得矩的替代估計的一致性的結(jié)果。對基于gauss白噪聲假設(shè)多元弱平穩(wěn)序列自回歸模型的均值、白噪聲的協(xié)方差陣的極大似然估計都有依分布收斂到多元正態(tài)分布的統(tǒng)計性質(zhì)。