systems_identification   3

[1010.2286] Divergence-based characterization of fundamental limitations of adaptive dynamical systems
"general problem of adaptively controlling and/or identifying a stochastic dynamical system, where our {em a priori} knowledge allows us to place the system in a subset of a metric space (the uncertainty set). We present an information-theoretic meta-theorem that captures the trade-off between the metric complexity (or richness) of the uncertainty set, the amount of information acquired online in the process of controlling and observing the system, and the residual uncertainty remaining after the observations have been collected. Following the approach of Zames, we quantify {em a priori} information by the Kolmogorov (metric) entropy of the uncertainty set, while the information acquired online is expressed as a sum of information divergences. The general theory is used to derive new minimax lower bounds on the metric identification error, as well as to give a simple derivation of the minimum time needed to stabilize an uncertain stochastic linear system."
systems_identification  control_theory_and_control_engineering  estimation  learning_theory  minimax  heard_the_talk  raginsky.maxim  in_NB 
october 2010 by cshalizi
Simultaneous Confidence Intervals for Impulse Response
"Inference about an impulse response is a multiple testing problem with serially correlated coefficient estimates. This paper provides a method to construct simultaneous confidence regions for impulse responses and conditional bands to examine significance levels of individual impulse response coefficients given propagation trajectories. The paper also shows how to constrain a subset of impulse response paths to anchor structural identification and how to formally test the validity of such identifying constraints. Simulation and empirical evidence illustrate the new techniques. A broad summary of asymptotic analytic formulas is provided to make the methods easy to implement with commonly available statistical software."
time_series  systems_identification  confidence_sets  statistics  macroeconomics  re:your_favorite_dsge_sucks 
july 2009 by cshalizi

related tags

confidence_sets  control_theory_and_control_engineering  estimation  heard_the_talk  in_nb  information_theory  learning_theory  macroeconomics  minimax  raginsky.maxim  re:your_favorite_dsge_sucks  statistics  time_series 

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