Maximum likelihood estimators for generalized Cauchy processes

被引：9

作者：

Konno, Hidetoshi ^{[1
]}

Watanabe, Fumitoshi

机构：

[1] Univ Tsukuba, Dept Risk Engn, Fac Syst & Informat Engn, Tsukuba, Ibaraki 3058573, Japan

[2] Tokyo Elect Power Co Ltd, R & D Ctr, Tsurumi Ku, Yokohama, Kanagawa 2308510, Japan

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2007年 / 48卷 / 10期

基金：

日本学术振兴会;

关键词：

D O I：

10.1063/1.2800162

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Maximum likelihood estimator (MLE) for a generalized Cauchy process (GCP) is studied with the aid of the method of information geometry in statistics. Our GCP is described by the Langevin equation with multiplicative and additive noises. The exact expressions of MLEs are given for the two cases that the two types of noises are uncorrelated and mutually correlated. It is shown that the MLEs for these two GCPs are free from divergence even in the parameter region wherein the ordinary moments diverge. The MLE relations can be regarded as a generalized fluctuation-dissipation theorem for the present Langevin equation. Availability of them and of some other higher order statistics is demonstrated theoretically and numerically. (C) 2007 American Institute of Physics.

引用

页数：19

共 50 条

[11] MAXIMUM-LIKELIHOOD ESTIMATORS FOR A CLASS OF GAUSSIAN PROCESSES
YAGODA, A
KURZ, L
IEEE TRANSACTIONS ON INFORMATION THEORY, 1970, 16 (01) : 131 - +
[12] STRONG CONSISTENCY OF MAXIMUM LIKELIHOOD ESTIMATORS FOR ARMA PROCESSES
RISSANEN, J
CAINES, PE
ANNALS OF STATISTICS, 1979, 7 (02): : 297 - 315
[13] Generalized Conditional Maximum Likelihood Estimators in the Large Sample Regime
Chaumette, Eric
Vincent, Francois
Renaux, Alexandre
Galy, Jerome
2018 26TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO), 2018, : 271 - 275
[14] A note on the maximum likelihood estimators for the location and scatter parameters of a multivariate Cauchy distribution
Arslan, O
Kent, JT
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1998, 27 (12) : 3007 - 3014
[15] On Bahadur asymptotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes
Kakizawa, Y
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2000, 85 (01) : 29 - 44
[16] PERFORMANCE OF THE MAXIMUM LIKELIHOOD ESTIMATORS FOR THE PARAMETERS OF MULTIVARIATE GENERALIZED GAUSSIAN DISTRIBUTIONS
Bombrun, Lionel
Pascal, Frederic
Tourneret, Jean-Yves
Berthoumieu, Yannick
2012 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2012, : 3525 - 3528
[17] BIAS CORRECTED MAXIMUM LIKELIHOOD ESTIMATORS FOR THE PARAMETERS OF THE GENERALIZED NORMAL DISTRIBUTION
Gul, Hasan Huseyin
Dogru, Fatma Zehra
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2024, 73 (04):
[18] MOMENT ESTIMATORS AND MAXIMUM LIKELIHOOD
SHENTON, LR
BIOMETRIKA, 1958, 45 (3-4) : 411 - 420
[19] INVARIANCE OF MAXIMUM LIKELIHOOD ESTIMATORS
ZEHNA, PW
ANNALS OF MATHEMATICAL STATISTICS, 1966, 37 (03): : 744 - &
[20] ITERATED MAXIMUM LIKELIHOOD ESTIMATORS
DUDEWICZ, EJ
ANNALS OF MATHEMATICAL STATISTICS, 1968, 39 (05): : 1773 - +

← 1 2 3 4 5 →