Some nonlinear statistical problems of a Poisson process
Some parameter estimation problems for hypoelliptic homogeneous Gaussian diffusions
Some problems of exponential smoothing
The paper deals with some practical problems connected with the classical exponential smoothing in time series. The fundamental theorem of the exponential smoothing is extended to the case with missing observations and an interpolation procedure in the framework of the exponential smoothing is described. A simple method of the exponential smoothing for multivariate time series is suggested.
Some Results About Averaging in Stochastic Approximation.
Some results for the quadratic analysis of Gaussian processes and applications
Some results on exponential families of Markov processes
Some results on the spectral analysis of nonstationary time series.
Some unresolved issued in non-linear population dynamics.
The Lyapunov exponent is a statistic that measures the sensitive dependence of the dynamic behaviour of a system on its initial conditions. Estimates of Lyapunov exponents are often used to characterize the qualitative population dynamics of insect time series. The methodology for estimation of the exponent for an observed, noisy, short ecological time series is still under development. Some progress has been made recently in providing measures of error for these exponents. Studies that do not account...
Současná ekonometrie jako součást matematiky
Spatial correlation of gene expression measures in tissue microarry core analysis.
Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction
We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory...
Spatial structure analysis using planar indices.
Spatial planar indices have become a useful tool to analyze patterns of points. Despite that, no simulation study has been reported in literature in order to analyze the behaviour of these quantities under different pattern structures. We present here an extensive Monte Carlo simulation study focused on two important indices: the Index of Dispersion and the Index of Cluster Size, usually used to detect lack of homogeneity in a spatial point model. Finally, an application is also presented.
Spatio-temporal modelling of a Cox point process sampled by a curve, filtering and Inference
The paper deals with Cox point processes in time and space with Lévy based driving intensity. Using the generating functional, formulas for theoretical characteristics are available. Because of potential applications in biology a Cox process sampled by a curve is discussed in detail. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test sets. A...
Special sequential estimation problems in Markov processes
Spectral analysis of ARMA processes by Prony's method
Spectral density estimation for -adic stationary processes
Spectral density estimation for stationary stable random fields
We consider a stationary symmetric stable bidimensional process with discrete time, having the spectral representation (1.1). We consider a general case where the spectral measure is assumed to be the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. We estimate the density of the absolutely continuous measure and the density on the lines.
Spectrum of randomly sampled multivariate ARMA models
The paper is devoted to the spectrum of multivariate randomly sampled autoregressive moving-average (ARMA) models. We determine precisely the spectrum numerator coefficients of the randomly sampled ARMA models. We give results when the non-zero poles of the initial ARMA model are simple. We first prove the results when the probability generating function of the random sampling law is injective, then we precise the results when it is not injective.
Spektralna karakteristika ekstrapolacije jedne klase stacionarnih slučajnih procesa
Spiked Dirichlet process priors for Gaussian process models.