Nonparametric estimation of the ratios of derivatives of a multivariate distribution density from dependent observations.
Nonparametric inference for discretely sampled Lévy processes
Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X is studied. An estimator of ρ is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of ρ over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.
Nonparametric prediction via mode.
Normal covariances
Note on approximate non-Gaussian filtering with nonlinear observation relation
Note on inappropriate trend and seasonal elimination
Note on Minimum Contrast Estimates for MARKOV-Processes.
Note sur les comptabilités markoviennes
Number of hidden states and memory: a joint order estimation problem for Markov chains with Markov regime
This paper deals with order identification for Markov chains with Markov regime (MCMR) in the context of finite alphabets. We define the joint order of a MCMR process in terms of the number k of states of the hidden Markov chain and the memory m of the conditional Markov chain. We study the properties of penalized maximum likelihood estimators for the unknown order (k, m) of an observed MCMR process, relying on information theoretic arguments. The novelty of our work relies in the joint...
On a Berry-Esseen type bound for the maximum likelihood estimator of a parameter for some stochastic partial differential equations.
On a class of estimators in a multivariate RCA(1) model
This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...
On a Criterion for the Selection of Models for Stationary Time Series.
On a method of estimating parameters in non-negative ARMA models
On a simple estimate of correlations of stationary random sequences
On a strongly consistent estimator of the squared L_2-norm of a function
A kernel estimator of the squared -norm of the intensity function of a Poisson random field is defined. It is proved that the estimator is asymptotically unbiased and strongly consistent. The problem of estimating the squared -norm of a function disturbed by a Wiener random field is also considered.
On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields *
Many statistical applications require establishing central limit theorems for sums/integrals or for quadratic forms , where Xt is a stationary process. A particularly important case is that of Appell polynomials h(Xt) = Pm(Xt), h(Xt,Xs) = Pm,n (Xt,Xs), since the “Appell expansion rank" determines typically the type of central limit theorem satisfied by the functionals ST(h), QT(h). We review and extend here to multidimensional indices, along lines conjectured in [F. Avram and M.S. Taqqu,...
On adaptive control of Markov chains using nonparametric estimation
Two adaptive procedures for controlled Markov chains which are based on a nonparametric window estimation are shown.
On an estimation problem for type I censored spatial Poisson processes
In this paper we consider the problem of estimating the intensity of a spatial homogeneous Poisson process if a part of the observations (quadrat counts) is censored. The actual problem has occurred during a court case when one of the authors was a referee for the defense.
On Bartlett's test for correlation between time series
An explicit formula for the correlation coefficient in a two-dimensional AR(1) process is derived. Approximate critical values for the correlation coefficient between two one-dimensional AR(1) processes are tabulated. They are based on Bartlett’s approximation and on an asymptotic distribution derived by McGregor. The results are compared with critical values obtained from a simulation study.
On calculation of stationary density of autoregressive processes
An iterative procedure for computation of stationary density of autoregressive processes is proposed. On an example with exponentially distributed white noise it is demonstrated that the procedure converges geometrically fast. The AR(1) and AR(2) models are analyzed in detail.