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Identification of Signal, Noise, and Indistinguishable Subsets in High-Dimensional Data Analysis
Two-Level Thresholding Signal detection False positive control False negative control Multiple testing Variable screening
2013/6/13
Motivated by applications in high-dimensional data analysis where strong signals often stand out easily and weak ones may be indistinguishable from the noise, we develop a statistical framework to pro...
Volatility Inference in the Presence of Both Endogenous Time and Microstructure Noise
It^o Process Realized Volatility Integrated Volatility Time Endogeneity Market Microstructure Noise
2013/5/2
In this article we consider the volatility inference in the presence of both market microstructure noise and endogenous time. Estimators of the integrated volatility in such a setting are proposed, an...
State estimation under non-Gaussian Levy noise: A modified Kalman filtering method
Kalman filter modified Kalman filter Non-Gaussiannoise L′evy noise state estimation data assimilation
2013/4/28
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian L\'evy noise is present, the conventional Kalman filter may fail to be effective d...
Hitting probabilities for systems of non-linear stochastic heat equations with additive noise
Hitting probabilities systems of non-linear stochastic heat equations space-time white noise capacity Hausdor measure
2009/6/12
We consider a system of d coupled non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional additive space-time whitenoise. We establish upper and lower bounds on hitting pro...