Abstract
The sequence of “regression fractile” estimates of the error distribution in linear models (developed by Bassett and Koenker) is shown to be tight in appropriate metric spaces of distribution functions. This result yields weak convergence to the transformed “Brownian Bridge” process in these spaces, and has obvious application to goodness-of-fit tests for the error distribution. It also suggests that using this estimate may be better than using the empirical distribution of residuals when applying “bootstrap” methods.
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© 1984 Springer-Verlag Berlin Heidelberg
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Portnoy, S. (1984). Tightness of the Sequence of Empiric C.D.F. Processes Defined from Regression Fractiles. In: Franke, J., Härdle, W., Martin, D. (eds) Robust and Nonlinear Time Series Analysis. Lecture Notes in Statistics, vol 26. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7821-5_13
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DOI: https://doi.org/10.1007/978-1-4615-7821-5_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96102-6
Online ISBN: 978-1-4615-7821-5
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