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.

Keywords: asymptotic distributional risk, diffusion process, MLE, Shrinkage estimator, Wiener process

@article{PS_2012__16__139_0, author = {Nkurunziza, S\'ev\'erien}, title = {Shrinkage strategies in some multiple multi-factor dynamical systems}, journal = {ESAIM: Probability and Statistics}, pages = {139--150}, publisher = {EDP-Sciences}, volume = {16}, year = {2012}, doi = {10.1051/ps/2010015}, mrnumber = {2946124}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2010015/} }

TY - JOUR AU - Nkurunziza, Sévérien TI - Shrinkage strategies in some multiple multi-factor dynamical systems JO - ESAIM: Probability and Statistics PY - 2012 SP - 139 EP - 150 VL - 16 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2010015/ DO - 10.1051/ps/2010015 LA - en ID - PS_2012__16__139_0 ER -

%0 Journal Article %A Nkurunziza, Sévérien %T Shrinkage strategies in some multiple multi-factor dynamical systems %J ESAIM: Probability and Statistics %D 2012 %P 139-150 %V 16 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2010015/ %R 10.1051/ps/2010015 %G en %F PS_2012__16__139_0

Nkurunziza, Sévérien. Shrinkage strategies in some multiple multi-factor dynamical systems. ESAIM: Probability and Statistics, Volume 16 (2012), pp. 139-150. doi : 10.1051/ps/2010015. http://archive.numdam.org/articles/10.1051/ps/2010015/

[1] 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. | MR

,[2] E. Saleh, Improved nonparametric estimation of location vector in a multivariate regression model. J. Nonparametr. Stat. 11 (1999) 51-78. | MR | Zbl

and .[3] Continuous Time Econometric Modelling. Oxford University Press, Oxford (1990).

,[4] Asymptotic theory of statistics and probability. Springer Science & Business Media, New York (2008). | MR | Zbl

,[5] On the distribution of general quadratic functions in normal vectors. Stat. Neerl. 41 (1987) 245-251. | MR | Zbl

,[6] Analyzing spatial structure of communities using the two-dimensional Poisson lognormal species abundance model. The American Naturalist 160 (2002) 60-73.

, , and ,[7] 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. | Zbl

,[8] Modern Multivariate Statistical Techniques : Regression, Classification, and Manifold Learning. Springer Science, Business Media, LLC (2008). | MR | Zbl

,[9] The statistical implication of pre-test and Stein-rule estimators in econometrics. Amsterdam, North Holland (1978). | MR | Zbl

and ,[10] Brownian Motion and Stochastic Calculus. Springer-Verlag, New York (1991). | MR | Zbl

and ,[11] Statistical Inference for Ergodic Diffusion Processes, in Springer Series in Statistics. Springer-Verlag, London (2004). | MR | Zbl

,[12] Statistics of Random Processes : Generale Theory I. Springer-Verlag, New York (1977). | Zbl

and ,[13] Statistics of Random Processes : Applications II. Springer-Verlag, New York (1978). | MR | Zbl

and ,[14] Shrinkage Drift Parameter Estimation for Multi-factor Ornstein-Uhlenbeck Processes. Appl. Stoch. Models Bus. Ind. 26 (2010) 103-124. | MR | Zbl

and ,[15] Diffusion in random media, in Surveys in Applied Mathematics, edited by J.B. Keller, D. McLaughlin and G. Papanicolaou. Plenum Press (1995) 205-255. | MR | Zbl

,*Cited by Sources: *