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Construction of automatic confidence intervals in nonparametric heteroscedastic regression by a moment-oriented bootstrap

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  • Sommerfeld, Volker

Abstract

We construct pointwise confidence intervals for regression functions. The method uses nonparametric kernel estimates and the moment-oriented bootstrap method of Bunke which is a wild bootstrap based on smoothed local estimators of higher order error moments. We show that our bootstrap consistently estimates the distribution of mh(x0) - m(xo). In the present paper we focus on fully data-driven procedures and prove that the confidence intervals give asymptotically correct coverage probabilities.

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  • Sommerfeld, Volker, 1997. "Construction of automatic confidence intervals in nonparametric heteroscedastic regression by a moment-oriented bootstrap," SFB 373 Discussion Papers 1997,22, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199722
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    1. Hardle, W. & Hall, P. & Marron, J., 1990. "Regression smoothing parameters that are not far from their optimum," LIDAM Discussion Papers CORE 1990009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Droge, Bernd, 1994. "Some Comments on Cross-Validation," SFB 373 Discussion Papers 1994,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Bunke, O. & Droge, B. & Polzehl, J., 1995. "Model Selection, Transformations and Variance Estimation in Nonlinear Regression," SFB 373 Discussion Papers 1995,52, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Hardle, W. & Marron, J., 1989. "Bootstrap Simultaneous Error Bars For Nonparametric Regression," LIDAM Discussion Papers CORE 1989023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    1. Sommerfeld, Volker, 1997. "Wild bootstrap versus moment-oriented bootstrap," SFB 373 Discussion Papers 1997,76, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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