## Trimmed Least Squares Estimation in the Linear Model (1980)

Venue: | J. Amer. Statist. Assoc |

Citations: | 30 - 0 self |

### BibTeX

@ARTICLE{Carroll80trimmedleast,

author = {Raymond J. Carroll},

title = {Trimmed Least Squares Estimation in the Linear Model},

journal = {J. Amer. Statist. Assoc},

year = {1980},

pages = {828--838}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider two methods of defining a regression analogue to a trimmed mean. The first was suggested by Koenker and Bassett and uses their concept of regression quantiles. that of a trimmed mean. Its asymptotic behavior is completely analogous to The second method uses residuals from a preliminary estimator. Its asymptotic behavior depends heavily on the preliminary estimate; it behaves, in general, quite differently than the estimator proposed by Koenker and Bassett, and it can be rather inefficient at the normal model even if the percent trimming is small. However, if the preliminary estimator is the average of the two regression quantiles used with Koenker and Bassett's estimator, then the first and second methods are asymptotically equivalent for sYmmetric error distributions. Key Words and Phrases: regression analogue, trimmed mean, regression quantile, preliminary estimator, linear model, trimmed least squares David Ruppert is an Assistant Professor and Raymond,J. Carroll an