In: Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability, 5 (1999), Nr. 5. pp. 873-906. ISSN 1350-7265
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Abstract
We consider nonparametric estimation of the coefficients, of atime-varying autoregressive process. Choosing an orthonormal wavelet basisrepresentation of the coefficient functions, the empirical wavelet coefficientsare derived from the time series data as the solution of a least squares minimizationproblem. In order to allow the coefficient functions to be of inhomogeneous regularity,we apply nonlinear thresholding to the empirical coefficients and obtain locally smoothedestimates of the coefficient functions. We show that the resulting estimators attain theusual minimax L_2-rates up to a logarithm factor, simultaneously in a large scale of Besovclasses.
Document type: | Article |
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Journal or Publication Title: | Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability |
Volume: | 5 |
Number: | 5 |
Place of Publication: | Aarhus |
Date Deposited: | 01 Jul 2016 07:47 |
Date: | 1999 |
ISSN: | 1350-7265 |
Page Range: | pp. 873-906 |
Faculties / Institutes: | The Faculty of Mathematics and Computer Science > Institut für Mathematik |
DDC-classification: | 510 Mathematics |
Uncontrolled Keywords: | Nonlinear thresholding; non-stationary processes; time series; time-varying autoregression; wavelet estimators |
Series: | Beiträge zur Statistik > Reports |