Browsing by Subject "Wavelets"

Now showing items 1-18 of 18

    • Article  

      A comparative simulation study of wavelet shrinkage estimators for Poisson counts 

      Besbeas, P.; De Feis, I.; Sapatinas, Theofanis (2004)
      Using computer simulations, the finite sample performance of a number of classical and Bayesian wavelet shrinkage estimators for Poisson counts is examined. For the purpose of comparison, a variety of intensity functions, ...
    • 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  

      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  

      Maximal functions and smoothness spaces in Lp(ℝd) 

      Kyriazis, George C. (1998)
      We study smoothness spaces generated by maximal functions related to the local approximation errors of integral operators. It turns out that in certain cases these smoothness classes coincide with the spaces Cαp (ℝd), 0 < ...
    • 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  

      Multilevel characterizations of anisotropic function spaces 

      Kyriazis, George C. (2005)
      We present a general method for extending decomposition systems of L 2(ℝd) to decomposition systems for the anisotropic Triebel-Lizorkin and Besov spaces, Fp,qα,s and Bp,qα,s, respectively, for the full range of the indexes. ...
    • 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  

      Non-linear approximation and interpolation spaces 

      Kyriazis, George C. (2001)
      We study n-term wavelet-type approximations in Besov and Triebel Lizorkin spaces. In particular, we characterize spaces of functions which have prescribed degree of n-term approximation in terms of interpolation spaces. ...
    • Article  

      Nonlinear spectral density estimation: Thresholding the correlogram 

      Paparoditis Efstathios, E.; Politis, Dimitris Nicolas (2012)
      Traditional kernel spectral density estimators are linear as a function of the sample autocovariance sequence. The purpose of this article is to propose and analyse two new spectral estimation methods that are based on the ...
    • Article  

      Nonlinear spectral density estimation: Thresholding the correlogramAAA 

      Paparoditis Efstathios, E.; Politis, Dimitris Nicolas (2012)
      Traditional kernel spectral density estimators are linear as a function of the sample autocovariance sequence. The purpose of this article is to propose and analyse two new spectral estimation methods that are based on 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 posterior median estimators of possibly sparse sequences 

      Bochkina, N.; Sapatinas, Theofanis (2005)
      We adopt the Bayesian paradigm and discuss certain properties of posterior median estimators of possibly sparse sequences. The prior distribution considered is a mixture of an atom of probability at zero and a symmetric ...
    • Article  

      Optimal testing for additivity in multiple nonparametric regression 

      Abramovich, F.; De Feis, I.; Sapatinas, Theofanis (2009)
      We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) non- adaptive and adaptive hypothesis testing procedures for additivity ...
    • Article  

      Short-term load forecasting: The similar shape functional time-series predictor 

      Paparoditis Efstathios, E.; Sapatinas, Theofanis (2013)
      A novel functional time-series methodology for shortterm load forecasting is introduced. The prediction is performed by means of a weighted average of past daily load segments, the shape of which is similar to the expected ...
    • Article  

      Wavelet density estimation for weighted data 

      Cutillo, L.; De Feis, I.; Nikolaidou, C.; Sapatinas, Theofanis (2014)
      We consider the estimation of a density function on the basis of a random sample from a weighted distribution. We propose linear and nonlinear wavelet density estimators, and provide their asymptotic formulae for mean ...
    • Article  

      Wavelet estimators in nonparametric regression: A comparative simulation study 

      Antoniadis, Anestis; Bigot, J.; Sapatinas, Theofanis (2001)
      Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as ...
    • Article  

      Wavelet instruments for efficiency gains in generalized method of moment models 

      Michis, A.; Sapatinas, Theofanis (2007)
      We propose a simple computational method in the context of generalized method of moments for improving the efficiency of regression coefficient estimates. The gains in efficiency arise by incorporating additional moment ...