On Shannon-McMillan's limit theorem for pairs of stationary random processes
On some estimation variances in spatial statistics
On some Mixture Distributions
The aim of this paper is to establish some mixture distributions that arise in stochastic processes. Some basic functions associated with the probability mass function of the mixture distributions, such as k-th moments, characteristic function and factorial moments are computed. Further we obtain a three-term recurrence relation for each established mixture distribution.
On stationarity of a multiple doubly stochastic model
On the approximation of some optimal sequential plan
On the asymptotic variance in the central limit theorem for particle filters
Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends...
On the asymptotic variance in the central limit theorem for particle filters
Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends...
On the autocorrelation function of a trended series.
Equations are derived for the autocorrelation function of a trended series. The special case of a linear trend is analysed in detail. It is shown that the zero of the autocorrelation function of a trended series is, in general, only dependent on the length of the series. This result is valid for stochastic and deterministic trends.
On the Bayes approach in general multiple autoregressive series
On the Bayesian estimation for the stationary Neyman-Scott point processes
The pure and modified Bayesian methods are applied to the estimation of parameters of the Neyman-Scott point process. Their performance is compared to the fast, simulation-free methods via extensive simulation study. Our modified Bayesian method is found to be on average 2.8 times more accurate than the fast methods in the relative mean square errors of the point estimates, where the average is taken over all studied cases. The pure Bayesian method is found to be approximately as good as the fast...
On the computation of the exact distribution of power divergence test statistics
In this paper we introduce several algorithms to generate all the vectors in the support of a multinomial distribution. Computational studies are carried out to analyze their efficiency with respect to the CPU time and to calculate their efficiency frontiers. The proposed algorithm is used to calculate exact distributions of power divergence test statistics under the hypothesis of uniformity. Finally, several exact power comparisons are done for different divergence statistics and families of alternatives...
On the concept of the asymptotic Rényi distances for random fields
The asymptotic Rényi distances are explicitly defined and rigorously studied for a convenient class of Gibbs random fields, which are introduced as a natural infinite-dimensional generalization of exponential distributions.
On the consistency of sieve bootstrap prediction intervals for stationary time series
In the article, we consider construction of prediction intervals for stationary time series using Bühlmann's [8], [9] sieve bootstrapapproach. Basic theoretical properties concerning consistency are proved. We extend the results obtained earlier by Stine [21], Masarotto and Grigoletto [13] for an autoregressive time series of finite order to the rich class of linear and invertible stationary models. Finite sample performance of the constructed intervals is investigated by computer simulations.
On the convergence of the ensemble Kalman filter
Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and bounds on the ensemble then give convergence.
On the detection of a finite binary sequence in the presence of an interfering binary sequence
On the effect of erroneous models on systems in presence of correlated disturbances and uncertain observations.
On the efficiency of procedures for estimation of parameters in ARIMA models.
The paper discusses the implementation of the Newton-Raphson iterative method of estimation of parameters in the autoregressive integrated moving average (ARIMA) models. The efficiency of this method has been compared with other well known methods of estimation.
On the equivalence of two methods for interpolation
On the error exponent for ergodic Markov source
On the estimation in a class of diffusion-type processes. Aplication for diffusion branching processes.
In this work a family of stochastic differential equations whose solutions are multidimensional diffusion-type (non necessarily markovian) processes is considered, and the estimation of a parametric vector θ which relates the coefficients is studied. The conditions for the existence of the likelihood function are proved and the estimator is obtained by continuously observing the process. An application for Diffusion Branching Processes is given. This problem has been studied in some special cases...