Asymptotically Sufficient Statistics in Nonparametric Regression Experiments with Correlated Noise

Andrew V. Carter

Journal of Probability and Statistics, 2009, vol. 2009, 1-19

Abstract:

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.

Date: 2009
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/JPS/2009/275308.pdf (application/pdf)
http://downloads.hindawi.com/journals/JPS/2009/275308.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:275308

DOI: 10.1155/2009/275308

Access Statistics for this article

More articles in Journal of Probability and Statistics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().