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Keywords
(17)
Asymptotic Normal
Diffusion Process
Estimating Equation
Gamma Distribution
Heavy Tailed Distribution
Hypothesis Test
Infinitesimal Generator
Invariant Distribution
Markov Process
Parameter Estimation
Spectral Decomposition
Spectrum
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Statistical Inference
Stochastic Differential Equation
Transition Density
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Statistical inference for reciprocal gamma diffusion process
Statistical inference for reciprocal gamma diffusion process,10.1016/j.jspi.2009.06.009,Journal of Statistical Planning and Inference,N. N. Leonenko,N
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Statistical inference for reciprocal gamma diffusion process
(
Citations: 3
)
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N. N. Leonenko
,
N. Šuvak
We consider the problem of
parameter estimation
for an ergodic diffusion with reciprocal gamma invariant distribution.
Spectral decomposition
of the
transition density
of such a
Markov process
is presented in terms of a finite number of discrete eigenfunctions (Bessel polynomials) and eigenfunctions related to a continuous part of the
spectrum
of the negative
infinitesimal generator
of reciprocal gamma diffusion. Consistency and asymptotical normality of proposed estimators are presented. Based on the Stein equation for reciprocal gamma diffusion and Bessel polynomials, the hypothesis testing procedure is considered.
Journal:
Journal of Statistical Planning and Inference  J STATIST PLAN INFER
, vol. 140, no. 1, pp. 3051, 2010
DOI:
10.1016/j.jspi.2009.06.009
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Citation Context
(2)
...However, the first results on statistical analysis of reciprocal gamma, Student and Fisher–Snedecor diffusion, which all have heavytailed invariant distributions, are quite new
3
4
5
6
...
F. Avram
,
et al.
Parameter estimation for Fisher–Snedecor diffusion
...For details on these systems of orthogonal polynomials we refer to MasjedJamei [
36
,
37
], Lesky [
31
], Leonenko and Šuvak [
30
], and Avram et al...
N. N. Leonenko
,
et al.
Statistical Inference for Student Diffusion Process
References
(33)
Minimum contrast estimation of random processes based on information of second and third orders
(
Citations: 4
)
V. V. Anh
,
N. N. Leonenko
,
L. M. Sakhno
Journal:
Journal of Statistical Planning and Inference  J STATIST PLAN INFER
, vol. 137, no. 4, pp. 13021331, 2007
On a class of minimum contrast estimators for fractional stochastic processes and fields
(
Citations: 13
)
V. V. Anh
,
N. N. Leonenko
,
L. M. Sakhno
Journal:
Journal of Statistical Planning and Inference  J STATIST PLAN INFER
, vol. 123, no. 1, pp. 161185, 2004
Series Expansions for the First Passage Distribution of WongPearson JumpDiffusions
(
Citations: 2
)
Florin Avram
,
Nikolai Leonenko
,
Landy Rabehasaina
Journal:
Stochastic Analysis and Applications  STOCHASTIC ANAL APPL
, vol. 27, no. 4, pp. 770796, 2009
FKG INEQUALITY FOR BROWNIAN MOTION AND STOCHASTIC DIFFERENTIAL EQUATIONS
(
Citations: 5
)
DAVID BARBATO
Stein's method for diffusion approximations
(
Citations: 28
)
A. D. Barbour
Journal:
Probability Theory and Related Fields  PROBAB THEORY RELAT FIELD
, vol. 84, no. 3, pp. 297322, 1990
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Citations
(3)
Parameter estimation for Fisher–Snedecor diffusion
F. Avram
,
N. N. Leonenko
,
N. Šuvak
Journal:
Statistics
, vol. 45, no. 1, pp. 2742, 2011
Statistical Inference for Student Diffusion Process
(
Citations: 2
)
N. N. Leonenko
,
N. Šuvak
Journal:
Stochastic Analysis and Applications  STOCHASTIC ANAL APPL
, vol. 28, no. 6, pp. 9721002, 2010
Parameter estimation for reciprocal gamma and Student diusion processes
N. N. Leonenko
,
N. Suvak
Published in 2009.