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Robust M-Estimation for Heavy Tailed Nonlinear AR-GARCH (with Supplemental Appendix C)
, 2011
"... All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
by an NSERC Discovery Grant.
, 2014
"... We study Ginzburg–Landau equations for a complex vector order parameter Ψ = (ψ+, ψ−) ∈ C2. We consider the Dirichlet problem in the disk in R2 with a symmetric, degree-one boundary condition, and study its stability, in the sense of the spectrum of the second variation of the energy. We find that t ..."
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We study Ginzburg–Landau equations for a complex vector order parameter Ψ = (ψ+, ψ−) ∈ C2. We consider the Dirichlet problem in the disk in R2 with a symmetric, degree-one boundary condition, and study its stability, in the sense of the spectrum of the second variation of the energy. We find
1Robust M-Estimation for Heavy Tailed Nonlinear AR-GARCH (with Supplemental Appendix C)
, 2011
"... We develop new tail-trimmed M-estimation methods for heavy tailed Nonlinear AR-GARCH models. Tail-trimming allows both identi…cation of the true parameter and asymptotic normality for nonlinear models with asymmetric errors. In heavy tailed cases the rate of convergence is in…nitesimally close to th ..."
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to the highest possible amongst M-estimators for a particular loss function, hence super- 12-convergence can be achieved in nonlinear AR models with in…nite variance errors, and arbitrarily near 12-convergence for GARCH with errors that have an in…nite fourth moment. We present a consistent estimator
1On the Identifiability of Overcomplete Dictionaries via the Minimisation Principle Underlying K-SVD
, 2013
"... This article gives theoretical insights into the performance of K-SVD, a dictionary learning algorithm that has gained significant popularity in practical applications. The particular question studied here is when a dictionary Φ ∈ Rd×K can be recovered as local minimum of the minimisation criterion ..."
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, that in expectation the generating dictionary can be recovered exactly as a local minimum of the K-SVD criterion if the coefficient distribution exhibits sufficient decay. This decay can be characterised by the coherence of the dictionary and the `1-norm of the coefficients. Based on the asymptotic results
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