This Title All WIREs
How to cite this WIREs title:
WIREs Comp Stat

The L2E method

Full article on Wiley Online Library:   HTML PDF

Can't access this content? Tell your librarian.

Abstract Estimation theory and practice is generally focused on maximum likelihood methodology, which boasts of claims of efficiency and widespread availability in software. Likelihood methods occasionally encounter problems with small sample sizes, or if the data are contaminated with outliers. The first problem can be addressed by regularization methods such as Bayesian estimation; the latter problem can be solved by using robust methodology such as the M‐estimator, for example. is a particular example of an M‐estimator. This article motivates its special properties and provides detailed examples that take advantage of those properties. Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Density Estimation

Two‐parameter L2E fit (red) superimposed on kernel estimate. The blue dotted line is the one‐parameter L2E fit shown in Figure 3.

[ Normal View | Magnified View ]

L2E surface for the two parameters θ = (µ, σ); here, .

[ Normal View | Magnified View ]

Two L2E fits superimposed on a kernel estimate.

[ Normal View | Magnified View ]

L2E criterion for mixture data with local minima at and 3.79.

[ Normal View | Magnified View ]

Kernel estimate of 1000 points from a mixture; see text for details. The true mixture (red dotted line) and single normal MLE fit (blue dotted line) are also depicted.

[ Normal View | Magnified View ]

The two three‐component normal fits with a kernel estimate.

[ Normal View | Magnified View ]

Two slices of the three‐parameter L2E criterion; see text for details.

[ Normal View | Magnified View ]

Five‐parameter L2E fit (blue) superimposed on kernel estimate (black dotted) and true mixture (red dotted).

[ Normal View | Magnified View ]

Related Articles

Statistical Methods

Browse by Topic

Statistical and Graphical Methods of Data Analysis > Density Estimation

Access to this WIREs title is by subscription only.

Recommend to Your
Librarian Now!

The latest WIREs articles in your inbox

Sign Up for Article Alerts