Confidence Corridors for Multivariate Generalized Quantile Regression
Bibliographic Data
| ID | 19417987 |
|---|---|
| Authors | Shih-Kang Chao (0000-0002-2303-8605, Humboldt-Universität zu Berlin), Katharina Proksch (0009-0000-2585-8052, Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany ()), Holger Dette (0000-0001-7048-474X, Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany ()), Wolfgang Karl Härdle (0000-0001-5600-3014, Ladislaus von Bortkiewicz Chair of Statistics, C.A.S.E. - Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany, and School of Business, Singapore Management University, Singapore, 178899, Singapore ()) |
| Year | 2017 |
| Volume | 35 |
| Issue | 1 |
| Pages | 70-85 |
| Publication date | 2017-01-02 |
| Open Access | No |
| Type | ARTICLE |
| Venue | Journal of Business and Economic Statistics (JOURNAL) |
| Journal identifiers | ISSN: 0735-0015 • E-ISSN: 1537-2707 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/07350015.2015.1054493 |
| OpenAlex | W2160234967 |
| Language | IT |
| References cited | 30 |
We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric estimator and the true function of interest, which follow after a series of approximation steps including a Bahadur representation, a new strong approximation theorem, and exponential tail inequalities for Gaussian random fields. As a byproduct we also obtain multivariate confidence corridors for the regression function in the classical mean regression. To deal with the problem of slowly decreasing error in coverage probability of the asymptotic confidence corridors, which results in meager coverage for small sample sizes, a simple bootstrap procedure is designed based on the leading term of the Bahadur representation. The finite-sample properties of both procedures are investigated by means of a simulation study and it is demonstrated that the bootstrap procedure considerably outperforms the asymptotic bands in terms of coverage accuracy. Finally, the bootstrap confidence corridors are used to study the efficacy of the National Supported Work Demonstration, which is a randomized employment enhancement program launched in the 1970s.
Asymptotic distribution · Confidence and prediction bands · Confidence interval · Coverage probability · Econometrics · Estimator · Multivariate statistics · Nonparametric regression · Nonparametric statistics · Quantile · Quantile regression · Statistics · Mathematics · Probabilistic and Robust Engineering Design · Statistical Methods and Bayesian Inference · Statistical Methods and Inference · Applied Mathematics
| Highly cited | No |
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