**systems_identification**3

[1010.2286] Divergence-based characterization of fundamental limitations of adaptive dynamical systems

october 2010 by cshalizi

"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

july 2009 by cshalizi

"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

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