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Second Order Hadamard Differentiability in Statistical Applications
Cramer-von Mises statistic goodness of fit test Hadamard differentiability limiting distribution linear models M-estimator statistical functionals uniform asymptotic linearity weighted empirical processes
2015/12/11
A formulation of the second-order Hadamard differentiability of (extended) statistical functionals and some related theoretical results are established. These results are applied to derive the limitin...
An Inverse Power Method for Nonlinear Eigenproblems with Applications in 1-Spectral Clustering and Sparse PCA
Inverse Power Method for Nonlinear Eigenproblems Applications 1-Spectral Clustering Sparse PCA
2011/3/2
Many problems in machine learning and statistics can be formulated as (generalized)eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding crit...
Applications of the quadratic covariation differentiation theory: variants of the Clark-Ocone and Stroock's formulas
the quadratic covariation differentiation theory the Clark-Ocone and Stroock's formulas
2010/11/11
In a 2006 article (\cite{A1}), Allouba gave his quadratic covariation differentiation theory for It\^o's integral calculus. He defined the derivative of a semimartingale with respect to a Brownian mo...