Models where the least trimmed squares and least median of squares estimators are maximum likelihood
The Least Trimmed Squares (LTS) and Least Median of Squares (LMS) estimators are popular robust regression estimators. The idea behind the estimators is to find, for a given h, a sub-sample of h good observations among n observations and estimate the regression on that sub-sample. We find models, ba...
| Main Authors: | , , |
|---|---|
| 格式: | Journal article |
| 语言: | English |
| 出版: |
2019
|
| _version_ | 1826260194150055936 |
|---|---|
| author | Berenguer-Rico, V Johansen, S Nielsen, B |
| author_facet | Berenguer-Rico, V Johansen, S Nielsen, B |
| author_sort | Berenguer-Rico, V |
| collection | OXFORD |
| description | The Least Trimmed Squares (LTS) and Least Median of Squares (LMS) estimators are popular robust regression estimators. The idea behind the estimators is to find, for a given h, a sub-sample of h good observations among n observations and estimate the regression on that sub-sample. We find models, based on the normal or the uniform distribution respectively, in which these estimators are maximum likelihood. We provide an asymptotic theory for the location-scale case in those models. The LTS estimator is found to be sqrt(h) consistent and asymptotically standard normal. The LMS estimator is found to be h consistent and asymptotically Laplace. |
| first_indexed | 2024-03-06T19:01:46Z |
| format | Journal article |
| id | oxford-uuid:13c7f56e-04d4-4021-bf13-fd0483efa8b1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:01:46Z |
| publishDate | 2019 |
| record_format | dspace |
| spelling | oxford-uuid:13c7f56e-04d4-4021-bf13-fd0483efa8b12022-03-26T10:15:48ZModels where the least trimmed squares and least median of squares estimators are maximum likelihoodJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:13c7f56e-04d4-4021-bf13-fd0483efa8b1EnglishSymplectic Elements at Oxford2019Berenguer-Rico, VJohansen, SNielsen, BThe Least Trimmed Squares (LTS) and Least Median of Squares (LMS) estimators are popular robust regression estimators. The idea behind the estimators is to find, for a given h, a sub-sample of h good observations among n observations and estimate the regression on that sub-sample. We find models, based on the normal or the uniform distribution respectively, in which these estimators are maximum likelihood. We provide an asymptotic theory for the location-scale case in those models. The LTS estimator is found to be sqrt(h) consistent and asymptotically standard normal. The LMS estimator is found to be h consistent and asymptotically Laplace. |
| spellingShingle | Berenguer-Rico, V Johansen, S Nielsen, B Models where the least trimmed squares and least median of squares estimators are maximum likelihood |
| title | Models where the least trimmed squares and least median of squares estimators are maximum likelihood |
| title_full | Models where the least trimmed squares and least median of squares estimators are maximum likelihood |
| title_fullStr | Models where the least trimmed squares and least median of squares estimators are maximum likelihood |
| title_full_unstemmed | Models where the least trimmed squares and least median of squares estimators are maximum likelihood |
| title_short | Models where the least trimmed squares and least median of squares estimators are maximum likelihood |
| title_sort | models where the least trimmed squares and least median of squares estimators are maximum likelihood |
| work_keys_str_mv | AT berenguerricov modelswheretheleasttrimmedsquaresandleastmedianofsquaresestimatorsaremaximumlikelihood AT johansens modelswheretheleasttrimmedsquaresandleastmedianofsquaresestimatorsaremaximumlikelihood AT nielsenb modelswheretheleasttrimmedsquaresandleastmedianofsquaresestimatorsaremaximumlikelihood |