Estimation of Affine Jump-Diffusions Using Realized Variance and Bipower Variation in Empirical Characteristic Function Method

2014 ◽  
Author(s):  
Alex Levin ◽  
Vladimir Khramtsov
Keyword(s):  
Characteristic Function ◽  
Function Method ◽  
Empirical Characteristic Function ◽  
Realized Variance ◽  
Jump Diffusions

scholarly journals Estimation of K–Distributed Clutter by using Characteristic Function Method

2012 ◽  
Author(s):  
Mohammad Hamiruce Marhaban
Keyword(s):  
Characteristic Function ◽  
Function Method ◽  
Maximum Likelihood Method ◽  
Radar System ◽  
Likelihood Method ◽  
Empirical Characteristic Function ◽  
Sea Clutter ◽  
Novel Approach ◽  
Simulation Results ◽  
Distribution Parameter Estimation

Prestasi pengesanan radar maritim selalunya terbatas disebabkan gema laut atau serakan yang tidak diingini. Taburan-K adalah salah satu ketumpatan berekor panjang, di mana ia dikenali dalam komuniti pemprosesan isyarat untuk memadan dengan tepat serakan laut. Dalam kertas kerja ini, satu pendekatan novel untuk menganggar parameter taburan-K dibentangkan. Kaedah ini diterbitkan dari fungsi ciri empirik komponen quadrature. Hasil simulasi menunjukkan pembaikan yang ketara dari segi kecenderungan dan varians teranggar, berbanding dengan manamana kaedah bukan kemungkinan maksimum sedia ada. Kata kunci: Sistem radar, serakan laut, taburan–K, penganggaran parameter, fungsi ciri Detection performance of the maritime radars is often limited by the unwanted sea echo or clutter. K-distribution is one of the long-tailed densities which is known in the signal processing community for fitting the radar sea clutter accurately. In this paper, a novel approach for estimating the parameter of K-distribution is presented. The method is derived from the empirical characteristic function of the quadrature components. Simulation results show a great improvement in term of estimated bias and variance, compared with any existing non-maximum likelihood method. Key words: Radar system, sea clutter, K–distribution, parameter estimation, 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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