×

zbMATH — the first resource for mathematics

Assessing model adequacy in possibly misspecified quantile regression. (English) Zbl 1365.62143
Summary: Possibly misspecified linear quantile regression models are considered. A measure for assessing the combined effect of several covariates on a certain conditional quantile function is proposed. The measure is based on an adaptation to quantile regression of the famous coefficient of determination originally proposed for mean regression, and compares a ‘reduced’ model to a ‘full’ model, both of which can be misspecified. An estimator of this measure is proposed and its asymptotic distribution is investigated both in the non-degenerate and the degenerate case. The finite sample performance of the estimator is studied through a number of simulation experiments. The proposed measure is also applied to a data set on body fat measures.

MSC:
62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
62P10 Applications of statistics to biology and medical sciences; meta analysis
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Angrist, J.; Chernozhukov, V.; Fernández-Val, I., Quantile regression under misspecification, with an application to the US wage structure, Econometrica, 74, 539-563, (2006) · Zbl 1145.62399
[2] Capizzi, M.; Leto, G.; Petrone, A.; Zampetti, S.; Papa, R. E.; Osimani, M.; Spoletini, M.; Lenzi, A.; Osborn, J.; Mastantuono, M.; Vania, A.; Buzzetti, R., Wrist circumference is a clinical marker of insulin resistance in overweight and obese children and adolescents, Circulation, 123, 1757-1762, (2011)
[3] Chen, K.; Ying, Z.; Zhang, H.; Zhao, L., Analysis of least absolute deviation, Biometrika, 95, 107-122, (2008) · Zbl 1437.62416
[4] Coutinho, T.; Goel, K.; de Corrêa, S. D.; Kragelund, C.; Kanaya, A. M.; Zeller, M.; Park, J. S.; Kober, L.; Torp-Pedersen, C.; Cottin, Y.; Lorgis, L.; Lee, S. H.; Kim, Y. J.; Thomas, R.; Roger, V. L.; Somers, V. K.; Lopez-Jimenez, F., Central obesity and survival in subjects with coronary artery disease: a systematic review of the literature and collaborative analysis with individual subject data, Journal of the American College of Cardiology, 57, 1877-1886, (2011)
[5] Dette, H.; Munk, A., Some methodological aspects of validation of models in nonparametric regression, Statistica Neerlandica, 57, 207-244, (2003) · Zbl 1090.62531
[6] Hodges, J. L.; Lehmann, E. L., Testing the approximative validity of statistical hypotheses, Journal of the Royal Statistical Society: Series B, 16, 261-268, (1954) · Zbl 0057.35403
[7] Kaw, A., Introduction to matrix algebra, (2011), Autar Kaw
[8] Kim, T.-W.; White, H., Estimation, inference and specification testing for possibly misspecified quantile regression, Advances in Econometrics, 17, 107-132, (2003)
[9] Koenker, R., (Quantile Regression, Econometric Society Monographs, vol. 38, (2005), Cambridge University Press Cambridge) · Zbl 1111.62037
[10] Koenker, R.; Bassett, G., Regression quantiles, Econometrica, 46, 33-50, (1978) · Zbl 0373.62038
[11] Koenker, R.; Machado, J. A., Goodness of fit and related inference processes for quantile regression, Journal of the American Statistical Association, 94, 1296-1310, (1999) · Zbl 0998.62041
[12] Mckean, J. W.; Sievers, G. L., Coefficient of determination for least absolute deviation analysis, Statistics & Probability Letters, 5, 49-54, (1987) · Zbl 0612.62105
[13] Noh, H., El Ghouch, A., Van Keilegom, I., 2012. Quality of fit measures in the framework of quantile regression. Scandinavian Journal of Statistics (in press). · Zbl 1259.62022
[14] Penrose, K.; Nelson, A.; Fisher, A., Generalized body composition prediction equation for men using simple measurement techniques, Medicine and Science in Sports and Exercise, 17, 189, (1985)
[15] Siri, W. E., Gross composition of the body, Advances in Biological and Medical Physics, 4, 239-280, (1956)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.