Shrinkage strategies in some multiple multi-factor dynamical systems
ESAIM: Probability and Statistics (2012)
- Volume: 16, page 139-150
- ISSN: 1292-8100
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topNkurunziza, Sévérien. "Shrinkage strategies in some multiple multi-factor dynamical systems." ESAIM: Probability and Statistics 16 (2012): 139-150. <http://eudml.org/doc/276391>.
@article{Nkurunziza2012,
abstract = {In this paper, we are interested in estimation problem for the drift parameters matrices of m independent multivariate diffusion processes. More specifically, we consider the case where the m-parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance of the established estimators. Further, we carry out simulation studies for observation periods of small and moderate lengths of time that corroborate the theoretical finding for which shrinkage estimators outperform over the MLE. The proposed method is useful in model assessment and variable selection. },
author = {Nkurunziza, Sévérien},
journal = {ESAIM: Probability and Statistics},
keywords = {Asymptotic distributional risk; diffusion process; MLE; Shrinkage estimator; Wiener process.; asymptotic distributional risk; shrinkage estimator; Wiener process},
language = {eng},
month = {7},
pages = {139-150},
publisher = {EDP Sciences},
title = {Shrinkage strategies in some multiple multi-factor dynamical systems},
url = {http://eudml.org/doc/276391},
volume = {16},
year = {2012},
}
TY - JOUR
AU - Nkurunziza, Sévérien
TI - Shrinkage strategies in some multiple multi-factor dynamical systems
JO - ESAIM: Probability and Statistics
DA - 2012/7//
PB - EDP Sciences
VL - 16
SP - 139
EP - 150
AB - In this paper, we are interested in estimation problem for the drift parameters matrices of m independent multivariate diffusion processes. More specifically, we consider the case where the m-parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance of the established estimators. Further, we carry out simulation studies for observation periods of small and moderate lengths of time that corroborate the theoretical finding for which shrinkage estimators outperform over the MLE. The proposed method is useful in model assessment and variable selection.
LA - eng
KW - Asymptotic distributional risk; diffusion process; MLE; Shrinkage estimator; Wiener process.; asymptotic distributional risk; shrinkage estimator; Wiener process
UR - http://eudml.org/doc/276391
ER -
References
top- S.E. Ahmed, Shrinkage estimation of regression coefficients from censored data with multiple observations, in Empirical Bayes and Likelihood inference, edited by S.E. Ahmed and N. Reid. Springer, New York (2001) 103–120.
- S.E. Ahmed and A.K.Md.E. Saleh, Improved nonparametric estimation of location vector in a multivariate regression model. J. Nonparametr. Stat.11 (1999) 51–78.
- A.R. Bergstrom, Continuous Time Econometric Modelling. Oxford University Press, Oxford (1990).
- A. DasGupta, Asymptotic theory of statistics and probability. Springer Science & Business Media, New York (2008).
- M.C.M. De Gunst, On the distribution of general quadratic functions in normal vectors. Stat. Neerl.41 (1987) 245–251.
- S. Engen, R. Lande, T. Wall and J.P. DeVries, Analyzing spatial structure of communities using the two-dimensional Poisson lognormal species abundance model. The American Naturalist160 (2002) 60–73.
- S. Iyengar, Diffusion models for neutral activity, in Statistics for the 21st Century : Methodologies for Applications of the Future, edited by C.R. Rao and G. Szekely. Marcel-Dekker (2000) 233–250.
- A.J. Izenman, Modern Multivariate Statistical Techniques : Regression, Classification, and Manifold Learning. Springer Science, Business Media, LLC (2008).
- G.G. Judge and M.E. Bock, The statistical implication of pre-test and Stein-rule estimators in econometrics. Amsterdam, North Holland (1978).
- I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus. Springer-Verlag, New York (1991).
- A.Y. Kutoyants, Statistical Inference for Ergodic Diffusion Processes, in Springer Series in Statistics. Springer-Verlag, London (2004).
- R.S. Liptser and A.N. Shiryaev, Statistics of Random Processes : Generale Theory I. Springer-Verlag, New York (1977).
- R.S. Liptser and A.N. Shiryaev, Statistics of Random Processes : Applications II. Springer-Verlag, New York (1978).
- S. Nkurunziza and S.E. Ahmed, Shrinkage Drift Parameter Estimation for Multi-factor Ornstein-Uhlenbeck Processes. Appl. Stoch. Models Bus. Ind.26 (2010) 103–124.
- G. Papanicolaou, Diffusion in random media, in Surveys in Applied Mathematics, edited by J.B. Keller, D. McLaughlin and G. Papanicolaou. Plenum Press (1995) 205–255.
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