Propriété asymptotique d’un modèle statistique pour une chaîne de Markov à valeurs dans
Propriétés asymptotiques presque sûres de l'estimateur des moindres carrés d'un modèle autorégressif vectoriel
Propriétés de mélange des processus autorégressifs polynomiaux
Propriétés du spectre évolutif d'un processus non stationnaire
QML estimators in linear regression models with functional coefficient autoregressive processes.
QMLE of periodic bilinear models and of PARMA models with periodic bilinear innovations
This paper develops an asymptotic inference theory for bilinear time series models with periodic coefficients . For this purpose, we establish firstly a necessary and sufficient conditions for such models to have a unique stationary and ergodic solutions (in periodic sense). Secondly, we examine the consistency and the asymptotic normality of the quasi-maximum likelihood estimator under very mild moment condition for the innovation errors. As a result, it is shown that whenever the model is...
Quadratic estimation from non-independent uncertain observations with coloured noise.
Recursive least-squares quadratic filtering and fixed-point smoothing algorithms for signal estimation from uncertain observations are derived when the uncertainty is modeled by not necessarily independent variables and the observations contain white plus coloured noise. The proposed estimators do not require the knowledge of the state-space of the model generating the signal, but only the moments, up to the fourth one, of the processes involved, along with the probability that the signal exists...
Quantification of prior knowledge about global characteristics of linear normal model
Quantitative convergence rates of Markov chains: A simple account.
Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points
2000 Mathematics Subject Classification: 60J60, 62M99.In this paper, we study the quasi-likelihood estimator of the drift parameter θ in the Ornstein-Uhlenbeck diffusion process, when the process is observed at random time points, which are assumed to be unobservable. These time points are arrival times of a Poisson process with known rate. The asymptotic properties of the quasi-likelihood estimator (QLE) of θ, as well as those of its approximations are also elucidated. An extensive simulation study...
Quasi-Maximum Likelihood Estimation of Parameters in a Multivariate Poisson Process.
Quelques exercices d'utilisation des critères de A. A. Markov
Quelques problèmes linéaires de statistique concernant un processus stochastique de moyenne inconnue
Quick Consistency of Quasi-Maximum Likelihood Estimators in a Multivariate Poisson Process.
Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood
We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility...
Random coefficients bifurcating autoregressive processes
This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton−Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency, with a convergence rate, and asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new results in both these frameworks.
Random perturbations of stochastic processes with unbounded variable length memory.
Random sequences with normal covariances
Rate of convergence for a class of RCA estimators
This work deals with Random Coefficient Autoregressive models where the error process is a martingale difference sequence. A class of estimators of unknown parameter is employed. This class was originally proposed by Schick and it covers both least squares estimator and maximum likelihood estimator for instance. Asymptotic behavior of such estimators is explored, especially the rate of convergence to normal distribution is established.
Ratio type statistics for detection of changes in mean