Maximum likelihood estimator of the volatility of forward rates driven by geometric spatial AR sheet.
Maximum likelihood principle and -divergence: continuous time observations
The paper investigates the relation between maximum likelihood and minimum -divergence estimates of unknown parameters and studies the asymptotic behaviour of the likelihood ratio maximum. Observations are assumed to be done in the continuous time.
Maximum likelihood principle and -divergence: discrete time observations
The paper investigates the relation between maximum likelihood and minimum -divergence estimates of unknown parameters and studies the asymptotic behaviour of the likelihood ratio maximum. Observations are assumed to be done in the discrete time.
Mean square error for histograms when estimating Radon-Nikodym derivatives.
Mean squared errors of prediction by kriging in linear models with errors.
Minimax and bayes estimation in deconvolution problem*
We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function εh where h ∈ L2(R1) and ε is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...
Minimax and Bayes estimation when the loss function is unknown
Minimax prediction of the sum of processes
Minimax results for estimating integrals of analytic processes
The problem of predicting integrals of stochastic processes is considered. Linear estimators have been constructed by means of samples at N discrete times for processes having a fixed Hölderian regularity s > 0 in quadratic mean. It is known that the rate of convergence of the mean squared error is of order N-(2s+1). In the class of analytic processes Hp, p ≥ 1, we show that among all estimators, the linear ones are optimal. Moreover, using optimal coefficient estimators derived through...
Minimax results for estimating integrals of analytic processes
Minimax sequential estimation for the multinomial and gamma processes
Minimax sequential estimation of parameters of random fields
Minimum distance estimator for a hyperbolic stochastic partial differentialequation
We study a minimum distance estimator in -norm for a class ofnonlinear hyperbolic stochastic partial differential equations, driven by atwo-parameter white noise. The consistency and asymptotic normality of thisestimator are established under some regularity conditions on thecoefficients. Our results are applied to the two-parameterOrnstein-Uhlenbeck process.
Mise en œuvre d'un modèle à coefficient aléatoire
Mixed parametrization for curved exponential models in homogeneous Markov processes with a finite state space.
Mixturas de distribuciones normales con aplicaciones a problemas estadísticos complejos.
Model and variable selection procedures for semiparametric time series regression.
Model selection for (auto-)regression with dependent data
In this paper, we study the problem of non parametric estimation of an unknown regression function from dependent data with sub-gaussian errors. As a particular case, we handle the autoregressive framework. For this purpose, we consider a collection of finite dimensional linear spaces (e.g. linear spaces spanned by wavelets or piecewise polynomials on a possibly irregular grid) and we estimate the regression function by a least-squares estimator built on a data driven selected linear space among...
Model selection for (auto-)regression with dependent data
In this paper, we study the problem of non parametric estimation of an unknown regression function from dependent data with sub-Gaussian errors. As a particular case, we handle the autoregressive framework. For this purpose, we consider a collection of finite dimensional linear spaces (e.g. linear spaces spanned by wavelets or piecewise polynomials on a possibly irregular grid) and we estimate the regression function by a least-squares estimator built on a data driven selected linear space among...
Modelado de series temporales con métodos en bloque y recursivos. Desarrollo de estimadores y predictores adaptativos.
En este artículo se presenta un análisis comparativo entre los algoritmos más interesantes para la estimación de parámetros de series temporales, tanto en bloque como recursivos. Se propone que los modelos autorregresivos largos constituyen una parametrización general para modelizar series inestables, cuyos parámetros pueden estimarse adecuadamente con algoritmos recursivos, tales como los filtros celosía.