Conference Agenda
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Mathematical Statistics Location: 1.012 Session Chair: Mathias Trabs | |
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Alternative argmin method in the non-unique case and application for gradual regression changes 1: University of Hamburg, Germany; 2: Charles University of Prague, Czech Republic Assume one wants to estimate the true parameter $\vartheta_0$, which is the {\it maximal} value {\it minimizing} a function $M(\vartheta)$ over $\vartheta$. Let $M_n(\vartheta)$ be a consistent estimator for $M(\vartheta)$ uniformly in $\vartheta$. Although uniform convergence holds, one cannot apply the argmin theorem in the non-unique minimum case. Using the {\it maximal} value {\it minimizing} the function $M_n(\vartheta)$ over $\vartheta$ generally does not give a consistent estimator. We consider a special case with real-valued parameter, and define a new consistent estimator. This method is then applied to estimate the gradual (smooth) change point $\vartheta_0$ of a nonparametric regression model $Y=m(X)+\varepsilon$ with real-valued covariates, and a continuous regression function $m$ with maximal value $\vartheta_0$, where $m$ is zero. | |
