Behavior of elemental sets in regression

David J. Olive; Douglas M. Hawkins

doi:10.1016/j.spl.2006.09.009

Behavior of elemental sets in regression

David J. Olive
, Douglas M. Hawkins

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Elemental sets are used to produce trial estimates b of the regression coefficients β . If b₀ minimizes ∥ b - β ∥ among all elemental fits b, then ∥ b₀ - β ∥ = O_P (n^{- 1}), regardless of the criterion used. For any estimator b_A, ∥ b_A - β ∥ is at best O_P (n^{- 1 / 2}) . Hence restricting fits to elemental introduces asymptotically negligible error.

Original language	English (US)
Pages (from-to)	621-624
Number of pages	4
Journal	Statistics and Probability Letters
Volume	77
Issue number	6
DOIs	https://doi.org/10.1016/j.spl.2006.09.009
State	Published - Mar 15 2007

Bibliographical note

Funding Information:
This research was supported by NSF Grants DMS 9806584 and DMS 0202922.

Keywords

Breakdown
Depth
LMS
LTA
Outliers
Robust regression

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10.1016/j.spl.2006.09.009

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@article{683598027f15435d82858dad461d3512,

title = "Behavior of elemental sets in regression",

abstract = "Elemental sets are used to produce trial estimates b of the regression coefficients β . If b0 minimizes ∥ b - β ∥ among all elemental fits b, then ∥ b0 - β ∥ = OP (n- 1), regardless of the criterion used. For any estimator bA, ∥ bA - β ∥ is at best OP (n- 1 / 2) . Hence restricting fits to elemental introduces asymptotically negligible error.",

keywords = "Breakdown, Depth, LMS, LTA, Outliers, Robust regression",

author = "Olive, \{David J.\} and Hawkins, \{Douglas M.\}",

note = "Funding Information: This research was supported by NSF Grants DMS 9806584 and DMS 0202922. ",

year = "2007",

month = mar,

day = "15",

doi = "10.1016/j.spl.2006.09.009",

language = "English (US)",

volume = "77",

pages = "621--624",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

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TY - JOUR

T1 - Behavior of elemental sets in regression

AU - Olive, David J.

AU - Hawkins, Douglas M.

N1 - Funding Information: This research was supported by NSF Grants DMS 9806584 and DMS 0202922.

PY - 2007/3/15

Y1 - 2007/3/15

N2 - Elemental sets are used to produce trial estimates b of the regression coefficients β . If b0 minimizes ∥ b - β ∥ among all elemental fits b, then ∥ b0 - β ∥ = OP (n- 1), regardless of the criterion used. For any estimator bA, ∥ bA - β ∥ is at best OP (n- 1 / 2) . Hence restricting fits to elemental introduces asymptotically negligible error.

AB - Elemental sets are used to produce trial estimates b of the regression coefficients β . If b0 minimizes ∥ b - β ∥ among all elemental fits b, then ∥ b0 - β ∥ = OP (n- 1), regardless of the criterion used. For any estimator bA, ∥ bA - β ∥ is at best OP (n- 1 / 2) . Hence restricting fits to elemental introduces asymptotically negligible error.

KW - Breakdown

KW - Depth

KW - LMS

KW - LTA

KW - Outliers

KW - Robust regression

UR - https://www.scopus.com/pages/publications/33847071950

UR - https://www.scopus.com/pages/publications/33847071950#tab=citedBy

U2 - 10.1016/j.spl.2006.09.009

DO - 10.1016/j.spl.2006.09.009

M3 - Article

AN - SCOPUS:33847071950

SN - 0167-7152

VL - 77

SP - 621

EP - 624

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 6

ER -

Behavior of elemental sets in regression

Abstract

Bibliographical note

Keywords

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