A Study of Blockwise Wavelet Estimates Via Lower Bounds for a Spike Function

Sam Efromovich

Scandinavian Journal of Statistics, 2005, vol. 32, issue 1, 133-158

Abstract: Abstract. A blockwise shrinkage is a popular adaptive procedure for non‐parametric series estimates. It possesses an impressive range of asymptotic properties, and there is a vast pool of blocks and shrinkage procedures used. Traditionally these estimates are studied via upper bounds on their risks. This article suggests the study of these adaptive estimates via non‐asymptotic lower bounds established for a spike underlying function that plays a pivotal role in the wavelet and minimax statistics. While upper‐bound inequalities help the statistician to find sufficient conditions for a desirable estimation, the non‐asymptotic lower bounds yield necessary conditions and shed a new light on the popular method of adaptation. The suggested method complements and knits together two traditional techniques used in the analysis of adaptive estimates: a numerical study and an asymptotic minimax inference.

Date: 2005
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/j.1467-9469.2005.00419.x

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:bla:scjsta:v:32:y:2005:i:1:p:133-158

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().