Browsing by Subject "Besov spaces"
Now showing items 120 of 21

Article
Compactly supported frames for spaces of distributions associated with nonnegative selfadjoint operators
(2014)A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and TriebelLizorkin spaces in the general setting of a doubling metric measure ...

Doctoral Thesis Open AccessOpen Access
Contributions to wavelet methods in nonparametric statistics
(Πανεπιστήμιο Κύπρου, Σχολή Θετικών και Εφαρμοσμένων Επιστημών / University of Cyprus, Faculty of Pure and Applied Sciences, 200908)Στο πρώτο κεφάλαιο ασχολούμαστε με το πρόβλημα της εκτίμησης του ολοκληρώματος του τετραγώνου μιας συνάρτησης πυκνότητας όταν δεδομένα με βάρος ειναι διαθέσιμα. Δείχνουμε ότι ο προτεινόμενος εκτιμητής επιτυγχάνει τη βέλτιστη ...

Article
Decomposition systems for function spaces
(2003)Let Θ := {θIe : e ∈ E, I ∈ D} be a decomposition system for L2(ℝd) indexed over D, the set of dyadic cubes in ℝd, and a finite set E, and let θ̃ := {θ̃Ie : e ∈ E, I ∈ D} be the corresponding dual functionals. That is, for ...

Article
Frequentist optimality of bayes factor estimators in wavelet regression models
(2007)We investigate the theoretical performance of Bayes factor estimators in wavelet regression models with independent and identically distributed errors that are not necessarily normally distributed. We compare these estimators ...

Article
Functional deconvolution in a periodic setting: Uniform case
(2009)We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where ...

Article
A functional waveletkernel approach for time series prediction
(2006)We consider the prediction problem of a time series on a whole time interval in terms of its past. The approach that we adopt is based on functional kernel nonparametric regression estimation techniques where observations ...

Article
Homogeneous Besov and Triebel–Lizorkin spaces associated to nonnegative selfadjoint operators
(2017)Homogeneous Besov and Triebel–Lizorkin spaces with complete set of indices are introduced in the general setting of a doubling metric measure space in the presence of a nonnegative selfadjoint operator whose heat kernel ...

Article
Inversion of noisy Radon transform by SVD based needlets
(2010)A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the ...

Article
Jacobi decomposition of weighted TriebelLizorkin and Besov spaces
(2008)The LittlewoodPaley theory is extended to weighted spaces of distributions on [1,1] with Jacobi weights w(t) = (1  t)α(1+t) β. Almost exponentially localized polynomial elements (needlets) {ρξ}, {ψξ} are constructed ...

Article
Minimax rates of convergence and optimality of bayes factor wavelet regression estimators under pointwise risks
(2009)We consider function estimation in nonparametric regression over Besov spaces and under pointwise lurisks (1 ≤ u < ∞). First we derive both nonadaptive and adaptive minimax pointwise rates of convergence in the standard ...

Article
Multichannel boxcar deconvolution with growing number of channels
(2011)We consider the problem of estimating the unknown response function in the multichannel deconvolution model with a boxcarlike kernel which is of particular interest in signal processing. It is known that, when the number ...

Article
Multichannel deconvolution with long range dependence: Upper bounds on the Lprisk (1 ≤ p < ∞)
(2015)We consider multichannel deconvolution in a periodic setting with longmemory errors under three different scenarios for the convolution operators, i.e., supersmooth, regularsmooth and boxcar convolutions. We investigate ...

Article
Multichannel deconvolution with longrange dependence: A minimax study
(2014)We consider the problem of estimating the unknown response function in the multichannel deconvolution model with longrange dependent Gaussian or subGaussian errors. We do not limit our consideration to a specific type ...

Article
New bases for TriebelLizorkin and Besov spaces
(2002)We give a new method for construction of unconditional bases for general classes of TriebelLizorkin and Besov spaces. These include the Lp, Hp, potential, and Sobolev spaces. The main feature of our method is that the ...

Article
Nonparametric regression estimation based on spatially inhomogeneous data: Minimax global convergence rates and adaptivity
(2014)We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known density g with a finite number of ...

Article
On convergence rates equivalency and sampling strategies in functional deconvolution models
(2010)Using the asymptotical minimax framework, we examine convergence rates equivalency between a continuous functional deconvolution model and its reallife discrete counterpart over a wide range of Besov balls and for the ...

Article
On pointwise optimality of Bayes factor wavelet regression estimators
(2006)We investigate the theoretical performance of Bayes factor estimators at a single point in wavelet regression models with independent and identically distributed errors that are not necessarily normally distributed. We ...

Article
On the estimation of the function and its derivatives in nonparametric regression: A bayesian testimation approach
(2011)We consider the problem of estimating the unknown response function and its deriva tives in the standard nonparametric regression model. Recently, Abramovich et al. (2010) applied a Bayesian testimation procedure in a ...

Article
Stochastic expansions in an overcomplete wavelet dictionary
(2000)We consider random functions defined in terms of members of an overcomplete wavelet dictionary. The function is modelled as a sum of wavelet components at arbitrary positions and scales where the locations of the wavelet ...

Article
Wavelet methods for continuoustime prediction using Hilbertvalued autoregressive processes
(2003)We consider the prediction problem of a continuoustime stochastic process on an entire timeinterval in terms of its recent past. The approach we adopt is based on the notion of autoregressive Hilbert processes that ...