Chang, Ziqing; Xue, Liugen; Zhu, Lixing On an asymptotically more efficient estimation of the single-index model. (English) Zbl 1190.62082 J. Multivariate Anal. 101, No. 8, 1898-1901 (2010). Summary: We revisit the single-index model with heteroscedastic errors, and recommend an estimating equation method in terms of transferring restricted least squares to unrestricted least squares: the estimator of the index parameter is asymptotically more efficient than existing estimators in the literature in the sense that it is of a smaller limiting variance. Cited in 24 Documents MSC: 62G08 Nonparametric regression and quantile regression 62G20 Asymptotic properties of nonparametric inference 62J05 Linear regression; mixed models Keywords:single-index model; asymptotical efficiency; least squares estimation PDFBibTeX XMLCite \textit{Z. Chang} et al., J. Multivariate Anal. 101, No. 8, 1898--1901 (2010; Zbl 1190.62082) Full Text: DOI References: [1] Brillinger, D. R., A Generalized linear model with “Gaussian” regressor variables, (Bickel, P. J.; Doksum, K. A.; Hodges, J. L., A Festschrift for Erich L. Lehmann (1983), Wadsworth: Wadsworth Belmont, CA), 97-114 [2] Hall, P., On projection pursuit regression, Ann. Statist., 17, 573-588 (1989) · Zbl 0698.62041 [3] Zhu, Lixing; Fang, Kai Tai, On projection pursuit approximation for nonparametric regresion, (Sen, P. S.; Salama, I. A., Proceedings of “Order Statistics and Nonparametrics: Theory and Applications” (1992)), 455-469 [4] H. Ichimura, Estimation of single index models. Ph.D. Dissertation, Dept. Economics, MIT, 1987.; H. Ichimura, Estimation of single index models. Ph.D. Dissertation, Dept. Economics, MIT, 1987. [5] Härdle, W.; Hall, P.; Ichimura, H., Optimal smoothing in single-index models, Ann. Statist., 21, 157-178 (1993) · Zbl 0770.62049 [6] Carroll, R. J.; Fan, J.; Gijbels, I.; Wand, M. P., Generalized partially linear single-index models, J. Amer. Statist. Assoc., 92, 477-489 (1997) · Zbl 0890.62053 [7] Xia, Y.; Härdle, W., Semi-parametric estimation of partially linear single index models, J. Multivariate Anal., 97, 1162-1184 (2006) · Zbl 1089.62050 [8] Ichimura, H., Semiparametric least squares (SLS) and weighted SLS estimation of singleindex models, J. Econometrics, 58, 71-120 (1993) · Zbl 0816.62079 [9] Xia, Y. C., Asymptotic distributions for two estimators of the single-index models, Econometric Theory, 22, 1112-1137 (2006) · Zbl 1170.62323 [10] Xia, Y.; Tong, H.; Li, W. K.; Zhu, L. X., An adaptive estimation of dimension reduction space, J. R. Stat. Soc. B, 64, 363-410 (2002) · Zbl 1091.62028 [11] Horowitz, J. L.; Härdle, W., Direct semiparametric estimation of single-index models with discrete covariates, J. Amer. Statist. Assoc., 91, 1632-1640 (1996) · Zbl 0881.62037 [12] Bickel, P.; Klaassen, C. A.J.; Ritov, Y.; Wellner, J., Efficient and Adaptive Inference in Semi-Parametric Models (1993), Johns Hopkins University Press: Johns Hopkins University Press Baltimore [13] Wang, J. L.; Xue, L. G.; Zhu, L. X.; Chong, Y. S., Estimation for a partial-linear single-index model, Ann. Statist., 38, 246-274 (2010) · Zbl 1181.62038 [14] Fan, J.; Gijbels, I., Local Polynomial Modeling and its Applications (1996), Chapman and Hall: Chapman and Hall London · Zbl 0873.62037 [15] Yu, Y.; Ruppert, D., Penalized spline estimation for partially linear single-index models, J, Amer. Statist. Assoc., 97, 1042-1054 (2002) · Zbl 1045.62035 [16] Xue, L. G.; Zhu, L. X., Empirical likelihood for single-index model, J. Mult. Anal., 97, 1295-1312 (2006) · Zbl 1099.62045 [17] Zhu, L. X.; Xue, L. G., Empirical likelihood confidence regions in a partially linear single-index model, J. R. Stat. Soc. B, 68, 549-570 (2006) · Zbl 1110.62055 [18] Hall, P.; Yao, Q., Approximating conditional distribution functions using dimension reduction, Ann. Statist., 33, 1404-1421 (2005) · Zbl 1072.62008 [19] Chiou, J. M.; Müller, H. G., Quasi-likelihood regression with unknown link and variance functions, J. Amer. Statist. Assoc., 93, 1376-1387 (1998) · Zbl 1065.62512 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.