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Scientific article
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English

Sensitivity and other properties of wavelet regression and density estimators

Contributors

Renaud, Olivier

Published in

Statistica sinica, vol. 12, no. 4, p. 1275-1290

Publication date

2002

Abstract

We give a unified, non-iterative formulation for wavelet estimators that can be applied in density estimation, regression on a regular grid and regression with a random design. This formulation allows us to better understand the bias due to a given method of coefficients estimation at high resolution. We also introduce functional representations for estimators of interest. The proposed formulation is well suited for the study of estimation bias and sensitivity analysis and, in the second part, we compute the influence function of various wavelet estimators. This tool allows us to see how the influence of observations can differ strongly depending on their locations. The lack of shift-invariance can be investigated and the influence function can be used to compare different approximation schemes for the wavelet estimator. We show that a local linear regression-type approximation for the higher resolution coefficients induces more extreme and variable influence of the observations on the final estimator than does the standard approximation. New approximation schemes are proposed.

Keywords

  • Approximation kernel
  • Influence function
  • Irregular design
  • Functional
  • Sensitivity to the design
  • Shift invariance

UNIGE affiliation entities

UNIGE research groups

Citation (ISO format)

RENAUD, Olivier. Sensitivity and other properties of wavelet regression and density estimators. In: Statistica sinica, 2002, vol. 12, n° 4, p. 1275–1290.

Main files (1)

Article (Published version)

Identifiers

  • PID : unige:17375

Additional URL for this publication

http://www3.stat.sinica.edu.tw/statistica/j12n4/j12n420/j12n420.htm

Journal ISSN

1017-0405
576views
187downloads

Technical informations

Creation

13/10/2011 09:16:00

First validation

13/10/2011 09:16:00

Update

14/10/2025 00:29:06

Status update

14/03/2023 17:04:03

Last indexation

30/05/2026 07:46:41
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