B0565
Title: Multiple cusp estimation in regression models
Authors: Maik Doering - University of Hohenheim (Germany) [presenting]
Abstract: The problem of estimating the locations of cusps in a regression model is considered. That means, we focus on regression functions, which are continuous, but not differentiable at a known number of unknown locations. We investigate the consistency with increasing sample size of the least squares estimates of the locations of the cusps. It turns out that the rates of convergence depend on the order of smoothness at the locations of the cusps and that our estimator converges to a maximizer of a Gaussian process. For a small order of smoothness at the cusps the least squares estimator for the location of the cusps shows a non-regular asymptotic. That means, we have not the asymptotic normality property, but a representation of the limit distribution as maximizer of a fractional Brownian motion with drift. In order to get confidence intervals for the least squares estimator the limit distribution will be simulated.
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