Nonparametric probability weighted empirical characteristic function and applications

2016 ◽  
Vol 108 ◽  
pp. 52-61 ◽  
Author(s):  
Simos G. Meintanis ◽  
Nikolai G. Ushakov
Keyword(s):  
Characteristic Function ◽  
Empirical Characteristic Function

On the first zero of an empirical characteristic function

1991 ◽  
Vol 28 (3) ◽  
pp. 593-601 ◽  
Author(s):  
H. U. Bräker ◽  
J. Hüsler
Keyword(s):  
Characteristic Function ◽  
Limit Distribution ◽  
Random Variable ◽  
Empirical Characteristic Function ◽  
The Real ◽  
Exponential Decrease ◽  
Characteristic Process

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

The Cumulant Generating Function Estimation Method

1997 ◽  
Vol 13 (2) ◽  
pp. 170-184 ◽  
Author(s):  
John L. Knight ◽  
Stephen E. Satchell
Keyword(s):  
Characteristic Function ◽  
Density Function ◽  
Generating Function ◽  
Estimation Method ◽  
Empirical Characteristic Function ◽  
Function Estimation ◽  
Asymptotic Equivalence ◽  
Cumulant Generating Function ◽  
Worked Example ◽  
Step Procedure

This paper deals with the use of the empirical cumulant generating function to consistently estimate the parameters of a distribution from data that are independent and identically distributed (i.i.d.). The technique is particularly suited to situations where the density function is unknown or unbounded in parameter space. We prove asymptotic equivalence of our technique to that of the empirical characteristic function and outline a six-step procedure for its implementation. Extensions of the approach to non-i.i.d. situations are considered along with a discussion of suitable applications and a worked example.

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