Efficient quantile estimation for functional-coefficient partially linear regression models

Abstract

The quantile estimation methods are proposed for functional-coefficient partially linear regression (FCPLR) model by combining nonparametric and functional-coefficient regression (FCR) model. The local linear scheme and the integrated method are used to obtain local quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.

Keywords

Functional-coefficient model / Quantile regression / Local linear method / Backfitting technique / Asymptotic normality

References

[1] Cai Z., Fan J., Yao Q.. Functional-coefficient regression models for nonlinear time series. J. Amer. Statist. Assoc., 2000, 95: 941-956

[2] Cai Z., Xu X.. Nonparametric quantile estimations for dynamic smooth coefficient models. J. Amer. Statist. Assoc., 2009, 104: 371-383

[3] Engle R., Granger C., Rice J. Semiparametric estimates of the relation between weather and electricity sales. J. Amer. Statist. Assoc., 1986, 81: 310-320

[4] Fan J., Gijbels I.. Local Polynomial Modelling and Its Applications, 1996, London: Chapment & Hall

[5] Härdle W., Liang H., Gao J.. Partially Linear Models, 2000, Berlin: Springer-Verlag

[6] Hastie T., Tibshirani R.. Varying-coefficient models. Roy. Statist. Soc., 1993, 55: 757-796

[7] Honda T.. Quantile regression in varying coefficient models. J. Statist. Plann. Inference, 2004, 121: 113-125

[8] Kim M.. Quantile Regression with varying coefficients. Ann. Statist., 2007, 35: 92-108

[9] Koenker R., Zhao Q.. Conditional quantile estimation and inference for ARCH models. Econometric Theory, 1996, 12: 793-813

[10] Linton O. B.. Efficient estimation of additive nonparametric regression models. Biometrika, 1997, 82: 93-100

[11] Mu Y., Wei Y.. A dynamic quantile regression transformation model for longitudinal data. Statist. Sin., 2009, 19: 1137-1153

[12] Wang H., Zhu Z., Zhou J.. Quantile regression in partially linear varying coefficient models. Ann. Statist., 2009, 37: 3841-3866

[13] Wong H., Zhang R., Ip W. C. Functional-coefficient partially regression model. J. Multivariate Anal., 2008, 99: 278-305

[14] Zhang W., Lee S.. Local polynomial fitting in semivarying coefficient models. J. Multivariate Anal., 2003, 82: 166-188