On asymptotic minimaxity of the adaptative kernel estimate of a density function
Displaying 181 – 200 of 298
On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators
Elena Di Bernardino, Didier Rullière (2013)
Dependence Modeling
We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these...
On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications
Silvia Vogel, Petr Lachout (2003)
Kybernetika
Part II of the paper aims at providing conditions which may serve as a bridge between existing stability assertions and asymptotic results in probability theory and statistics. Special emphasis is put on functions that are expectations with respect to random probability measures. Discontinuous integrands are also taken into account. The results are illustrated applying them to functions that represent probabilities.
On continuous convergence and epi-convergence of random functions. Part I: Theory and relations
Silvia Vogel, Petr Lachout (2003)
Kybernetika
Continuous convergence and epi-convergence of sequences of random functions are crucial assumptions if mathematical programming problems are approximated on the basis of estimates or via sampling. The paper investigates “almost surely” and “in probability” versions of these convergence notions in more detail. Part I of the paper presents definitions and theoretical results and Part II is focused on sufficient conditions which apply to many models for statistical estimation and stochastic optimization....
On cumulative process model and its statistical analysis
Petr Volf (2000)
Kybernetika
The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator of the...
On EM algorithms and their proximal generalizations
Stéphane Chrétien, Alfred O. Hero (2008)
ESAIM: Probability and Statistics
In this paper, we analyze the celebrated EM algorithm from the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure introduced in [Chretien and Hero (1998)] and called Kullback-proximal algorithms. The proximal framework allows us to prove new results concerning the cluster points. An essential contribution is a detailed analysis of the case where some cluster points lie on the boundary of the parameter space.
On estimating the diffusion coefficient : parametric versus nonparametric
Marc Hoffmann (2001)
Annales de l'I.H.P. Probabilités et statistiques
On estimating the memory for finitarily markovian processes
Gusztáv Morvai, Benjamin Weiss (2007)
Annales de l'I.H.P. Probabilités et statistiques
On Estimation of Hazard Function
S. S. Fazal (1982)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane
Tomáš Mrkvička, Jan Rataj (2009)
Kybernetika
A method of estimation of intrinsic volume densities for stationary random closed sets in based on estimating volumes of tiny collars has been introduced in T. Mrkvička and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch. Proc. Appl. 118 (2008), 2, 213-231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation radii in the...
On -estimators viewed as -estimators
Jan Šindelář (1994)
Kybernetika
On Median Unbiased Estimates.
J. Pfanzagl (1972)
Metrika
On Minimum Distance Estimators for Unimodel Densities.
R.D. Reiss (1976)
Metrika
On nonparametric estimators of location of maximum
Z. Hlávka (2011)
Acta Universitatis Carolinae. Mathematica et Physica
On pointwise adaptive curve estimation based on inhomogeneous data
Stéphane Gaïffas (2007)
ESAIM: Probability and Statistics
We want to recover a signal based on noisy inhomogeneous data (the amount of data can vary strongly on the estimation domain). We model the data using nonparametric regression with random design, and we focus on the estimation of the regression at a fixed point x0 with little, or much data. We propose a method which adapts both to the local amount of data (the design density is unknown) and to the local smoothness of the regression function. The procedure consists of a local polynomial...
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
Vasily G. Voinov, Mikhail Nikulin (1994)
Kybernetika
On some properties of estimators of a probability density
M. A. Mirzakhmedov, Sh. A. Chashimov (1973)
Kybernetika
On strong laws of large numbers for arrays of rowwise independent random elements.
Bozorgnia, Abolghassem, Patterson, Ronald Frank, Taylor, Robert Lee (1993)
International Journal of Mathematics and Mathematical Sciences
On testing of general random closed set model hypothesis
Tomáš Mrkvička (2009)
Kybernetika
A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set with values in the extended convex ring is introduced. The method is based on the summary statistics – normalized intrinsic volumes densities of the -parallel sets to . The estimated summary statistics are compared with theirs envelopes produced from simulations of the model given by the tested hypothesis. The p-level of the test is then computed via approximation...
On the adaptive wavelet estimation of a multidimensional regression function under -mixing dependence: Beyond the standard assumptions on the noise
Christophe Chesneau (2013)
Commentationes Mathematicae Universitatis Carolinae
We investigate the estimation of a multidimensional regression function from observations of an -mixing process , where , represents the design and the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of in its construction) or it is supposed that is bounded or/and has a known distribution. In this paper, we go far beyond this classical framework....