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Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion

Luís Ramos (2010)

Discussiones Mathematicae Probability and Statistics

When a diffusion is ergodic its transition density converges to its invariant density, see Durrett (1998). This convergence enabled us to introduce a sample partitioning technique that gives in each sub-sample, maximum likelihood estimators. The averages of these being a natural choice as estimators. To compare our estimators with the optimal we obtained from martingale estimating functions, see Sørensen (1998), we used the Ornstein-Uhlenbeck process for which exact simulations can be carried out....

Schémas de discrétisation anticipatifs et estimation du paramètre de dérive d'une diffusion

Sandie Souchet Samos (2010)

ESAIM: Probability and Statistics

Let YT = (Yt)t∈[0,T] be a real ergodic diffusion process which drift depends on an unkown parameter θ 0 ∈ ℝ p . Our aim is to estimate θ0 from a discrete observation of the process YT, (Ykδ)k=0,n, for a fixed and small δ, as T = nδ goes to infinity. For that purpose, we adapt the Generalized Method of Moments (see Hansen) to the anticipative and approximate discrete-time trapezoidal scheme, and then to Simpson's. Under some general assumptions, the trapezoidal scheme (respectively Simpson's scheme)...

Shrinkage strategies in some multiple multi-factor dynamical systems

Sévérien Nkurunziza (2012)

ESAIM: Probability and Statistics

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...

Shrinkage strategies in some multiple multi-factor dynamical systems

Sévérien Nkurunziza (2012)

ESAIM: Probability and Statistics

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...

Smoothness of Metropolis-Hastings algorithm and application to entropy estimation

Didier Chauveau, Pierre Vandekerkhove (2013)

ESAIM: Probability and Statistics

The transition kernel of the well-known Metropolis-Hastings (MH) algorithm has a point mass at the chain’s current position, which prevent direct smoothness properties to be derived for the successive densities of marginals issued from this algorithm. We show here that under mild smoothness assumption on the MH algorithm “input” densities (the initial, proposal and target distributions), propagation of a Lipschitz condition for the iterative densities can be proved. This allows us to build a consistent...

Stationary distribution of absolute autoregression

Jiří Anděl, Pavel Ranocha (2005)

Kybernetika

A procedure for computation of stationary density of the absolute autoregression (AAR) model driven by white noise with symmetrical density is described. This method is used for deriving explicit formulas for stationary distribution and further characteristics of AAR models with given distribution of white noise. The cases of Gaussian, Cauchy, Laplace and discrete rectangular distribution are investigated in detail.

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