Quality of fit measures in the framework of quantile regression

Noh, Hohsuk [UCL] El Ghouch, Anouar [UCL] Van Keilegom, Ingrid [UCL]

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.

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Document type	Article de périodique (Journal article) – Article de recherche
Access type	Accès libre
Publication date	2013
Language	Anglais
Journal information	"Scandinavian Journal of Statistics : theory and applications" - Vol. 40, no.1, p. 105-118 (2013)
Peer reviewed	yes
Publisher	Wiley-Blackwell Publishing Ltd. ((United Kingdom) Oxford)
issn	0303-6898
e-issn	1467-9469
Publication status	Publié
Affiliation	UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords	coefficient of determination ; inadequacy index ; lack-of-fit measure ; local polynomial estimation ; non-parametric regression ; quantile regression
Links	http://hdl.handle.net/2078.1/127025[Handle] https://doi.org/10.1111/j.1467-9469.2012.00792.x[DOI]

1. Chamberlain Gary, Quantile regression, censoring, and the structure of wages, Advances in Econometrics ISBN:9781139052030 p.171-210, 10.1017/ccol0521444594.005
2. Chaudhuri Probal, Doksum Kjell, Samarov Alexander, On average derivative quantile regression, 10.1214/aos/1031833670
3. Doksum Kjell, Samarov Alexander, Nonparametric Estimation of Global Functionals and a Measure of the Explanatory Power of Covariates in Regression, 10.1214/aos/1176324307
4. El Ghouch , A. Genton , M. G. Bouezmarni , T. 2010 Measuring the discrepancy of a parametric model via local polynomial smoothing
5. Kiefer J., On Bahadur's Representation of Sample Quantiles, 10.1214/aoms/1177698690
6. Kim Tae-Hwan, White Halbert, ESTIMATION, INFERENCE, AND SPECIFICATION TESTING FOR POSSIBLY MISSPECIFIED QUANTILE REGRESSION, Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later ISBN:0762310758 p.107-132, 10.1016/s0731-9053(03)17005-3
7. Koenker Roger, Machado José A. F., Goodness of Fit and Related Inference Processes for Quantile Regression, 10.1080/01621459.1999.10473882
8. Kong Efang, Linton Oliver, Xia Yingcun, UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL, 10.1017/s0266466609990661
9. Linton Oliver, Second Order Approximation in the Partially Linear Regression Model, 10.2307/2171722
10. Masry Elias, MULTIVARIATE LOCAL POLYNOMIAL REGRESSION FOR TIME SERIES:UNIFORM STRONG CONSISTENCY AND RATES, 10.1111/j.1467-9892.1996.tb00294.x
11. McKean Joseph W, Sievers Gerald L, Coefficients of determination for least absolute deviation analysis, 10.1016/0167-7152(87)90026-5
12. Powell James L., Stoker Thomas M., Optimal bandwidth choice for density-weighted averages, 10.1016/0304-4076(95)01761-5
13. Tong, Statist. Sinica, 10, 751 (2000)
14. Van Keilegom Ingrid, Wang Lan, Semiparametric modeling and estimation of heteroscedasticity in regression analysis of cross-sectional data, 10.1214/09-ejs547

See also
	[boreal:88440]	Quality of fit measures in the framework of quantile regression