On minimaxity of block thresholded wavelets under elliptical symmetry

H. Doosti*, A. Iranmanesh, M. Arashi, S. M. M. Tabatabaey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ρ-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block threshoding are investigated under elliptical symmetry. It is found that the estimators achieve optimal minimax convergence rates over a large classes of functions that involve many irregularities of a wide variety of types, including chirp and Doppler functions and jump discontinuities. Furthermore, the asymptotic results are robust with respect to non-normality.

Original languageEnglish
Pages (from-to)1526-1534
Number of pages9
JournalJournal of Statistical Planning and Inference
Volume141
Issue number4
DOIs
Publication statusPublished - Apr 2011
Externally publishedYes

Keywords

  • Block thresholded
  • Elliptically contoured distribution
  • Inverse-Laplace transform
  • Minimax estimation splines
  • Non-linear wavelet-based estimator
  • Rates of convergence

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