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Quality of Fit Measures in the Framework of Quantile Regression
Author(s) -
NOH HOHSUK,
GHOUCH ANOUAR EL,
KEILEGOM INGRID VAN
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2012.00792.x
Subject(s) - mathematics , quantile regression , covariate , quantile , statistics , context (archaeology) , measure (data warehouse) , parametric statistics , econometrics , regression analysis , computer science , data mining , paleontology , biology
. In regression experiments, to learn about the strength of the relationship between a covariate vector and a dependent variable, we propose a ‘coefficient of determination’ based on the quantiles. Such a coefficient is a ‘local’ measure in the sense that the strength is measured at a prespecified quantile level. Once estimated, it can be used, for example, to measure the relative importance of a subset of covariates in the quantile regression context. Related to this coefficient, we also propose a new ‘local’ lack‐of‐fit measure of a given parametric model. We provide some asymptotic results of the proposed measures and carry out a Monte Carlo simulation study to illustrate their use and performance in practice.