Final project for STAT 771 - Computational Statistics
Abstract: We cover fundamental principles of the Kernel Density Estimate (KDE) in a computational setting. Influence of kernel choice and bandwidth tuning on the density estimates are illustrated. Asymptotic bounds and decision theoretic frameworks are presented for the KDE. Computational complexity and efficiency of the Fast Fourier Transform (FFT) procedure in KDE calculation are shown, and bandwidth choices are also shown to nearly attain the asymptotic lower bound computationally. Multivariate extensions of the univariate first principles are briefly mentioned.
Keywords: nonparametric, statistics, fast fourier transform, curse of dimensionality