Asymptotic Expansions for Studentized M-Estimators With Applications to Multiple Comparisons

Consider the one-way layout with Y(,ij) being the i-th observation from group j, j = 1(1)p, i = 1(1)n(,j). Let N denote the total number of observations. Assume Y(,ij) = (theta)(,j) + e(,ij), where the e's are independent random disturbances with a common symmetric, but not necessarily normal,(, ) distribution. M-estimates of location and scale, (theta) and (sigma), are defined as(, )^roots of the equations (SIGMA)(,i)(psi)((Y(,ij)-(theta)(,j))/(sigma)) = 0, j = 1(1)(,p) and (SIGMA)(,j)(SIGMA)(,i)(chi)((Y(,ij)-(theta)(,j))/(sigma)) = C. The Studentized location statistics T(,j) = ((theta)(,j)-(theta)(,j))/(tau)(,j), where (tau)(,j) estimates the standard error of (theta)(,j), have a limiting N(,p)(O,I) distribution, but the small sample behavior is generally unknown.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Ringland, James Thomas

• Mathematics

Language dc:language

eng

Identifier

(UMI)AAI8108640

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/68179