Browsing by Subject "Besov spaces"

Now showing items 1-20 of 21

    • Article  

      Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators 

      Dekel, S.; Kerkyacharian, G.; Kyriazis, George C.; Petrushev, P. (2014)
      A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure ...
    • Doctoral Thesis  Open AccessOpen Access

      Contributions to wavelet methods in nonparametric statistics 

      Petsa, Athanasia A. (Πανεπιστήμιο Κύπρου, Σχολή Θετικών και Εφαρμοσμένων Επιστημών / University of Cyprus, Faculty of Pure and Applied Sciences, 2009-08)
      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 

      Kyriazis, George C. (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 

      Pensky, M.; Sapatinas, Theofanis (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 

      Pensky, M.; Sapatinas, Theofanis (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 wavelet-kernel approach for time series prediction 

      Antoniadis, Anestis; Paparoditis Efstathios, E.; Sapatinas, Theofanis (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 non-negative self-adjoint operators 

      Georgiadis, Athanasios G.; Kerkyacharian, G.; Kyriazis, George C.; Petrushev, P. (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 non-negative self-adjoint operator whose heat kernel ...
    • Article  

      Inversion of noisy Radon transform by SVD based needlets 

      Kerkyacharian, G.; Kyriazis, George C.; Le Pennec, E.; Petrushev, P.; Picard, D. (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 Triebel-Lizorkin and Besov spaces 

      Kyriazis, George C.; Petrushev, P.; Xu, Y. (2008)
      The Littlewood-Paley 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 

      Bochkina, N.; Sapatinas, Theofanis (2009)
      We consider function estimation in nonparametric regression over Besov spaces and under pointwise lu-risks (1 ≤ u < ∞). First we derive both non-adaptive and adaptive minimax pointwise rates of convergence in the standard ...
    • Article  

      Multichannel boxcar deconvolution with growing number of channels 

      Pensky, M.; Sapatinas, Theofanis (2011)
      We consider the problem of estimating the unknown response function in the multichannel deconvolution model with a boxcar-like ker-nel 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 Lp-risk (1 ≤ p < ∞) 

      Kulik, R.; Sapatinas, Theofanis; Wishart, J. R. (2015)
      We consider multichannel deconvolution in a periodic setting with long-memory errors under three different scenarios for the convolution operators, i.e., super-smooth, regular-smooth and box-car convolutions. We investigate ...
    • Article  

      Multichannel deconvolution with long-range dependence: A minimax study 

      Benhaddou, R.; Kulik, R.; Pensky, M.; Sapatinas, Theofanis (2014)
      We consider the problem of estimating the unknown response function in the multichannel deconvolution model with long-range dependent Gaussian or sub-Gaussian errors. We do not limit our consideration to a specific type ...
    • Article  

      New bases for Triebel-Lizorkin and Besov spaces 

      Kyriazis, George C.; Petrushev, P. (2002)
      We give a new method for construction of unconditional bases for general classes of Triebel-Lizorkin 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 

      Antoniadis, Anestis; Pensky, M.; Sapatinas, Theofanis (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 

      Pensky, M.; Sapatinas, Theofanis (2010)
      Using the asymptotical minimax framework, we examine convergence rates equivalency between a continuous functional deconvolution model and its real-life discrete counterpart over a wide range of Besov balls and for the ...
    • Article  

      On pointwise optimality of Bayes factor wavelet regression estimators 

      Bochkina, N.; Sapatinas, Theofanis (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 

      Petsa, A.; Sapatinas, Theofanis (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 

      Abramovich, F.; Sapatinas, Theofanis; Silverman, B. W. (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 continuous-time prediction using Hilbert-valued autoregressive processes 

      Antoniadis, Anestis; Sapatinas, Theofanis (2003)
      We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on the notion of autoregressive Hilbert processes that ...