• Article  

      Empirical Bayes approach to block wavelet function estimation 

      Abramovich, F.; Besbeas, P.; Sapatinas, Theofanis (2002)
      Wavelet methods have demonstrated considerable success in function estimation through term-by-term thresholding of the empirical wavelet coefficients. However, it has been shown that grouping the empirical wavelet coefficients ...
    • Article  

      On Bayesian testimation and its application to wavelet thresholding 

      Abramovich, F.; Grinshtein, V.; Petsa, A.; Sapatinas, Theofanis (2010)
      We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori testimation procedure of Abramovich et al. (2007) ...
    • 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  

      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 analysis and its statistical applications 

      Abramovich, F.; Bailey, T. C.; Sapatinas, Theofanis (2000)
      In recent years there has been a considerable development in the use of wavelet methods in statistics. As a result, we are now at the stage where it is reasonable to consider such methods to be another standard tool of the ...
    • Article  

      Wavelet thresholding via a Bayesian approach 

      Abramovich, F.; Sapatinas, Theofanis; Silverman, B. W. (1998)
      We discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression. A prior distribution is imposed on the wavelet coefficients of the unknown response function, designed ...