Současné vývojové směry matematické statistiky
Souvislost výsledků přijímacího řízení s úspěšností studia na MFF
Spannweitenpläne für messende Prüfung im doppelten Wahrscheinlichkeitsnetz.
Sparsity in penalized empirical risk minimization
Let (X, Y) be a random couple in S×T with unknown distribution P. Let (X1, Y1), …, (Xn, Yn) be i.i.d. copies of (X, Y), Pn being their empirical distribution. Let h1, …, hN:S↦[−1, 1] be a dictionary consisting of N functions. For λ∈ℝN, denote fλ:=∑j=1Nλjhj. Let ℓ:T×ℝ↦ℝ be a given loss function, which is convex with respect to the second variable. Denote (ℓ•f)(x, y):=ℓ(y; f(x)). We study the following penalized empirical risk minimization problem which is an empirical version of the problem (hereɛ≥0...
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 scan statistics adjusted for multiple clusters.
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.
Spatially adaptive density estimation by localised Haar projections
Given a random sample from some unknown density we devise Haar wavelet estimators for with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen and Spokoiny (Ann. Statist.25(1997) 927–947)). We show that these estimators satisfy an oracle inequality that adapts to heterogeneous smoothness of , simultaneously for every point in a fixed interval, in sup-norm loss. The thresholding constants involved in the test procedures can be chosen in practice under...
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 issue: Asymptotic statistics
Special issue: Editorial
Special sequential estimation problems in Markov processes
Special structures of mixed linear models with nuisance parameters
Specifying and simulating complex models using Bassist.
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