scholarly journals Asymptotic Normality of Hill’s Estimator under Weak Dependence

2020 ◽  
Author(s):  
Boualam Karima ◽  
Berkoun Youcef
Keyword(s):  
Asymptotic Normality ◽  
Weak Dependence ◽  
Hill’S Estimator

On the asymptotic normality of Hill's estimator

1995 ◽  
Vol 118 (2) ◽  
pp. 375-382 ◽  
Author(s):  
Sándor Csörgő ◽  
László Viharos
Keyword(s):  
Distribution Function ◽  
Asymptotic Normality ◽  
Order Statistics ◽  
Random Variables ◽  
Fixed Number ◽  
Distribution Functions ◽  
Independent Random Variables ◽  
Hill’S Estimator ◽  
Common Distribution ◽  
Common Distribution Function

Let X, X1, X2, …, be independent random variables with a common distribution function F(x) = P {X ≤ x}, x∈ℝ, and for each n∈ℕ, let X1, n ≤ … ≤ Xn, n denote the order statistics pertaining to the sample X1, …, Xn. We assume that 1–F(x) = x−1/cl(x), 0 < x < ∞, where l is some function slowly varying at infinity and c > 0 is any fixed number. The class of all such distribution functions will be denoted by .

Hill's estimator under weak dependence

2017 ◽  
Vol 46 (18) ◽  
pp. 9218-9229 ◽  
Author(s):  
Karima Boualam ◽  
Youcef Berkoun
Keyword(s):  
Weak Dependence ◽  
Hill’S Estimator

Asymptotic normality of processes with a branching structure

1998 ◽  
Vol 14 (4) ◽  
pp. 833-848
Author(s):  
Malcolm P. Quine ◽  
Władysław Szczotka
Keyword(s):  
Asymptotic Normality
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