Asymptotically Sufficient Statistics in Nonparametric Regression Experiments with Correlated Noise
Author
Source
Journal of Probability and Statistics
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-01-26
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
We find asymptotically sufficient statistics that could help simplify inference in nonparametric regression problems with correlated errors.
These statistics are derived from a wavelet decomposition that is used to whiten the noise process and to effectively separate high-resolution and low-resolution components.
The lower-resolution components contain nearly all the available information about the mean function, and the higher-resolution components can be used to estimate the error covariances.
The strength of the correlation among the errors is related to the speed at which the variance of the higher-resolution components shrinks, and this is considered an additional nuisance parameter in the model.
We show that the NPR experiment with correlated noise is asymptotically equivalent to an experiment that observes the mean function in the presence of a continuous Gaussian process that is similar to a fractional Brownian motion.
These results provide a theoretical motivation for some commonly proposed wavelet estimation techniques.
American Psychological Association (APA)
Carter, Andrew V.. 2010. Asymptotically Sufficient Statistics in Nonparametric Regression Experiments with Correlated Noise. Journal of Probability and Statistics،Vol. 2009, no. 2009, pp.1-19.
https://search.emarefa.net/detail/BIM-459551
Modern Language Association (MLA)
Carter, Andrew V.. Asymptotically Sufficient Statistics in Nonparametric Regression Experiments with Correlated Noise. Journal of Probability and Statistics No. 2009 (2009), pp.1-19.
https://search.emarefa.net/detail/BIM-459551
American Medical Association (AMA)
Carter, Andrew V.. Asymptotically Sufficient Statistics in Nonparametric Regression Experiments with Correlated Noise. Journal of Probability and Statistics. 2010. Vol. 2009, no. 2009, pp.1-19.
https://search.emarefa.net/detail/BIM-459551
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-459551