Abstract
A parametric estimation problem is considered in a misspecified regression model, where the regression function has a smooth change point. The focus lies on regression functions, which are continuous at the change point. Here, it is not assumed that the true regression function belongs to the model class. However, there exists a pseudo change point, such that the related regression function gives a reasonable approximation. With increasing sample size the asymptotic behavior is investigated of the least squares estimates of the change point. The consistency of the change point estimator for the pseudo estimator is shown. It turns out that the rate of convergence depends on the order of smoothness of the regression function at the change point.
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The author would like to thank the Associate Editor and Reviewer for their careful reading and comments. These comments and suggestions have been helpful for revising and improving the manuscript.
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Döring, M. (2015). Rate of Convergence of a Change Point Estimator in a Misspecified Regression Model. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_6
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DOI: https://doi.org/10.1007/978-3-319-13881-7_6
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