×

Two-step generalised empirical likelihood inference for semiparametric models. (English) Zbl 1162.62039

Summary: This paper shows how the generalised empirical likelihood method can be used to obtain valid asymptotic inference for the finite dimensional component of semiparametric models defined by a set of moment conditions. The results of the paper are illustrated using three well-known semiparametric regression models: partially linear single index, linear transformations with random censoring, and quantile regression with random censoring. Monte Carlo simulations suggest that some of the proposed test statistics have competitive finite sample properties. The results of the paper are applied to test for functional misspecification in a hedonic price model of a housing market.

MSC:

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62G08 Nonparametric regression and quantile regression
65C05 Monte Carlo methods
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Newey, W.; Smith, R., Higher order properties of GMM and generalized empirical likelihood estimators, Econometrica, 72, 219-256 (2004) · Zbl 1151.62313
[2] Owen, A., Empirical likelihood ratio confidence intervals for a single functional, Biometrika, 36, 237-249 (1988) · Zbl 0641.62032
[3] Qin, J.; Lawless, J., Empirical likelihood and general estimating equations, Annals of Statistics, 22, 300-325 (1994) · Zbl 0799.62049
[4] Owen, A., Empirical Likelihood (2001), Chapman and Hall · Zbl 0989.62019
[5] Efron, B., Nonparametric standard errors and confidence intervals, Canadian Journal of Statistics, 9, 139-172 (1981), with discussion · Zbl 0482.62034
[6] Imbens, G.; Spady, R.; Johnson, P., Information theoretic approaches to inference in moment condition models, Econometrica, 66, 333-357 (1998) · Zbl 1055.62512
[7] Owen, A., Empirical likelihood for linear models, Annals of Statistics, 19, 1725-1747 (1991) · Zbl 0799.62048
[8] Hansen, L.; Heaton, J.; Yaron, A., Finite sample properties of some alternative GMM estimators, Journal of Business and Economic Statistics, 14, 262-280 (1996)
[9] White, H., Maximum likelihood estimation of misspecified models, Econometrica, 50, 1-25 (1982) · Zbl 0478.62088
[10] Qin, G.; Tsao, M., Empirical likelihood inference for median regression models for censored survival data, Journal of Multivariate Analysis, 85, 416-430 (2003) · Zbl 1016.62112
[11] N. Hjort, I. McKeague, I. Van Keilegom, Extending the scope of empirical likelihood, Annals of Statistics (2009) (forthcoming); N. Hjort, I. McKeague, I. Van Keilegom, Extending the scope of empirical likelihood, Annals of Statistics (2009) (forthcoming) · Zbl 1160.62029
[12] Lu, W.; Liang, Y., Empirical likelihood inference for linear transformation model, Journal of Multivariate Analysis, 97, 1586-1599 (2006) · Zbl 1102.62108
[13] Xue, L.; Zhu, L., Empirical likelihood for single index models, Journal of Multivariate Analysis, 97, 1295-1312 (2006) · Zbl 1099.62045
[14] Baggerly, K. A., Empirical likelihood as a goodness of fit measure, Biometrika, 85, 535-547 (1998) · Zbl 0918.62043
[15] Guggenberger, P.; Smith, R., Generalized empirical likelihood estimators and tests under partial, weak and strong identification, Econometric Theory, 21, 667-709 (2005) · Zbl 1083.62086
[16] Barro, R., Unanticipated money growth and unemployment in the United States, American Economic Review, 82, 101-115 (1977)
[17] Neyman, J., Optimal asymptotic test of composite statistical hypothesis, (Probability and Statistics: the Harald Cramer Volume (1959), Almqvist and Wiksell), 213-234
[18] Rao, J.; Scott, A., The analysis of categorical data from complex sampling surveys: Chi-squared tests for goodness of fit and independence in two-way tables, Journal of the American Statistical Association, 76, 221-230 (1981) · Zbl 0473.62010
[19] Fan, J.; Gijbels, I., Local Polynomial Modeling and its Applications (1996), Chapman and Hall · Zbl 0873.62037
[20] Cox, D., Regression models and life tables, Journal of the Royal Statistical Society, 34, 187-220 (1972) · Zbl 0243.62041
[21] Chen, K.; Jin, Z.; Ying, Z., Semiparametric analysis of transformation models with censored data, Biometrika, 89, 659-668 (2002) · Zbl 1039.62094
[22] Ying, S.; Jung, S.; Wei, L., Survival analysis with median regression models, Journal of the American Statistical Association, 90, 178-184 (1995) · Zbl 0818.62103
[23] Kaplan, E.; Meier, P., Nonparametric estimation from incomplete data, Journal of the American Statistical Association, 53, 457-481 (1958) · Zbl 0089.14801
[24] Xia, T.; Härdle, W., Semiparametric estimation of partially linear single index models, Journal of Multivariate Analysis, 97, 1162-1184 (2006) · Zbl 1089.62050
[25] Rosen, S., Hedonic prices and implicit markets: Product differentiation in perfect competition, Journal of Political Economy, 82, 53-76 (1974)
[26] Anglin, P.; Gencay, R., Semiparametric estimation of a hedonic price function, Journal of Applied Econometrics, 11, 633-648 (1996)
[27] Whang, Y.; Andrews, D., Tests for specification for semiparametric and semiparametric models, Journal of Econometrics, 57, 277-318 (1993) · Zbl 0786.62029
[28] Wang, J., A note on the uniform consistency of the Kaplan-Meier estimator, Annals of Statistics, 15, 1313-1316 (1987) · Zbl 0631.62043
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.