Thesis

Year: 2008 Author: Galen Papkov, PhD Advisor: David W. Scott Committee Members: Dennis Cox, Richard Tapia Thesis Title: Locally-Adaptive Polynomial-Smoothed Histograms with Application to Massive and Pre-Binned Data Sets Abstract: This dissertation improves upon the smoothed polynomial histogram through the addition of a weight matrix to be more faithful to information obtained from high-density bins, the use of B-splines which are more numerically stable than truncated power functions, the implementation of P-splines with a difference penalty which is simpler to code compared to a roughness penalty and increases computational efficiency, and quadratic programming to compensate for occasional negativity within the estimated densities. A multivariate extension will be introduced via tensor products of B-splines. Applications exist in density estimation, bump hunting, and change-point analysis.

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