|Table of Contents|

Depth-Weighted LSE for Linear Regression Model and the Fit-Test(PDF)

《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2008年03期
Page:
39-43
Research Field:
数学
Publishing date:

Info

Title:
Depth-Weighted LSE for Linear Regression Model and the Fit-Test
Author(s):
Fan Yunzheng1Lin Lu2
1.School of Science,Nantong University,Nantong 226007,China
Keywords:
robustness statistica l dep th depth-w eigh ted LSE
PACS:
O212.1
DOI:
-
Abstract:
The ordinary Least Squares Estim ate ( LSE) in linear regress ion model is no t robust form any cases. A c lass o f projection-based depth functions, depth-w e ighted m ean and depth-w e ighted LSE w ere studied. These estim ates had desirable robustness. The prob lem of testing the fit of linear regression m ode l under the depth-w e ighted LSE w ere a lso d iscussed.

References:

[ 1] Godambe V P. Estim ating Functions[M ] . Oxfo rd: C larendon Press, 1991.
[ 2] Tukey JW. M athem atics and picturing data[ J]. Proc Intern CongrM ath V ancouver, 1975, 2( 2): 523-531.
[ 3] Liu R Y. On a notion of data depth based on random s imp lices[ J]. Ann Sta tist, 1990, 18( 2): 405-414.
[ 4] Zuo Y J, Se rfling R. Gene ra l notions o f statistica l depth function[ J]. Ann S tatist, 2000a, 28( 2): 461-482.
[ 5] Zuo Y J, Se rfling R. Structura l properties and convergence results for contours o f samp le statistical depth func tions[ J]. Ann Sta tist, 2000b, 28( 2) : 483-499.
[ 6] Zuo Y J, Cu iH J, H eX M. On the stahe-l Donoho estim a to r and depth-we ighted m eans ofm ultivariate data[ J] . Ann Statist,2004, 32( 1): 167-188.
[ 7] Lin L, ChenM H. Robust estim ating equation based on sta tistica l depth[ J]. Statistical Pape rs, 2006, 47( 2): 263-278
[ 8] Rousseeuw P J, H ubertM. Regression depth[ J]. JASA, 1999, 94: 389-433.
[ 9] Jeffrey D H a rt. Non Param etric Smoo th ing and Lack-o-f F it Tests[M ]. New York, Ber lin, H e ide lberg: Spr ing er-Ve rlag,1977.
[ 10] H oe ffdingW, Robb ins H. The centra l lim it theo rem for dependent random var iables[ J]. DukeM a th J, 1948, 15( 3): 773-780.

Memo

Memo:
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Last Update: 2013-05-05