Équations aux dérivées partielles associées à un problème de filtrage non linéaire
Estimation dans de la loi de certains processus à accroissements indépendants
Estimation of anisotropic gaussian fields through Radon transform
We estimate the anisotropic index of an anisotropic fractional brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional brownian field and prove that these processes admit...
Estimation of anisotropic Gaussian fields through Radon transform
We estimate the anisotropic index of an anisotropic fractional Brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional Brownian field and prove that these processes...
Exact representations for tumour incidence for some density-dependent models.
Exponential smoothing for irregular data
Various types of exponential smoothing for data observed at irregular time intervals are surveyed. Double exponential smoothing and some modifications of Holt’s method for this type of data are suggested. A real data example compares double exponential smoothing and Wright’s modification of Holt’s method for data observed at irregular time intervals.
Exponential smoothing for irregular time series
The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright’s modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order m for irregular data is derived. A similar method using a DLS **discounted least squares** estimation of polynomial trend of order m is derived as well. Maximum likelihood parameters estimation for forecasting...
Exponential smoothing for time series with outliers
Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this concept is applied...