Abstract
| Original language | English |
|---|---|
| Place of Publication | Tilburg |
| Publisher | Finance |
| Number of pages | 26 |
| Volume | 2003-23 |
| Publication status | Published - 2003 |
Publication series
| Name | CentER Discussion Paper |
|---|---|
| Volume | 2003-23 |
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Keywords
- ranking
- statistics
- regression analysis
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Serial and Nonserial Sign-and-Rank Statistics : Asymptotic Representation and Asymptotic Normality. / Hallin, M.; Vermandele, C.; Werker, B.J.M.
Tilburg : Finance, 2003. (CentER Discussion Paper; Vol. 2003-23).Research output: Working paper › Discussion paper › Other research output
TY - UNPB
T1 - Serial and Nonserial Sign-and-Rank Statistics
T2 - Asymptotic Representation and Asymptotic Normality
AU - Hallin, M.
AU - Vermandele, C.
AU - Werker, B.J.M.
N1 - Pagination: 26
PY - 2003
Y1 - 2003
N2 - The classical theory of rank-based inference is entirely based either on ordinary ranks, which do not allow for considering location nor intercept parameters, or on signed ranks, which require an assumption of symmetry.If the median, in the absence of a symmetry assumption, is considered as a location parameter, the maximal invariance property of ordinary ranks is lost to the ranks and the signs.As shown in Hallin and Werker (2003), conditioning on a maximal invariant in such situations is essential if semiparametric efficiency is to be reached.This new maximal invariant thus suggests a new class of statistics, based on ordinary ranks and signs.An asymptotic representation theory a la H ajek is developed here for such statistics, both in the nonserial and in the serial case.The corresponding asymptotic normality results clearly show how the signs are adding a separate contribution to the asymptotic variance, hence, potentially, to asymptotic e ciency.Applications to semiparametric inference in regression and time series models with median restrictions are treated in detail in a companion paper (Hallin, Werker, and Vermandele 2003).
AB - The classical theory of rank-based inference is entirely based either on ordinary ranks, which do not allow for considering location nor intercept parameters, or on signed ranks, which require an assumption of symmetry.If the median, in the absence of a symmetry assumption, is considered as a location parameter, the maximal invariance property of ordinary ranks is lost to the ranks and the signs.As shown in Hallin and Werker (2003), conditioning on a maximal invariant in such situations is essential if semiparametric efficiency is to be reached.This new maximal invariant thus suggests a new class of statistics, based on ordinary ranks and signs.An asymptotic representation theory a la H ajek is developed here for such statistics, both in the nonserial and in the serial case.The corresponding asymptotic normality results clearly show how the signs are adding a separate contribution to the asymptotic variance, hence, potentially, to asymptotic e ciency.Applications to semiparametric inference in regression and time series models with median restrictions are treated in detail in a companion paper (Hallin, Werker, and Vermandele 2003).
KW - ranking
KW - statistics
KW - regression analysis
M3 - Discussion paper
VL - 2003-23
T3 - CentER Discussion Paper
BT - Serial and Nonserial Sign-and-Rank Statistics
PB - Finance
CY - Tilburg
ER -