Minimax Linear Smoothers

Helge Blaker

Scandinavian Journal of Statistics, 2001, vol. 28, issue 1, 151-160

Abstract: We consider the problem of estimating the mean of a multivariate distribution. As a general alternative to penalized least squares estimators, we consider minimax estimators for squared error over a restricted parameter space where the restriction is determined by the penalization term. For a quadratic penalty term, the minimax estimator among linear estimators can be found explicitly. It is shown that all symmetric linear smoothers with eigenvalues in the unit interval can be characterized as minimax linear estimators over a certain parameter space where the bias is bounded. The minimax linear estimator depends on smoothing parameters that must be estimated in practice. Using results in Kneip (1994), this can be done using Mallows' CL‐statistic and the resulting adaptive estimator is now asymptotically minimax linear. The minimax estimator is compared to the penalized least squares estimator both in finite samples and asymptotically.

Date: 2001
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/1467-9469.00229

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:28:y:2001:i:1:p:151-160

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 ().