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Colloquium Talk, Duy Nguyen, Marist College

Date: Tuesday, September 12, 2017

Location: Rocky 300

Time:  12:30

Title: Nonparametric Density Estimation by B-Spline Duality and Applications

Abstract:

In this talk, we propose a new non-parametric density estimator derived from the theory of frames and Riesz bases. In particular, we propose the so-called biorthogonal density estimator based on the class of B-splines. This generalizes the traditional orthogonal series approach to density estimation by relaxing the orthogonality condition of the underlying basis. We also determine the approximate asymptotic optimal bandwidth for our newly proposed nonparametric estimator. Detailed analysis and comparison of our estimator with traditional nonparametric estimators and also the recently proposed approach in Botev et al. (2010) are presented. Applications to nonparametric simulation and empirical options pricing are also illustrated.