On the Equivalence Among Time Series Parameter Estimation, Approximation Theory, and Control Theory.
STANFORD UNIV CALIF DEPT OF STATISTICS
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The paper aims to lay the groundwork for establishing equivalences among such diverse topics as filtering, control, solution of integral equations abstract methods of analyzing partial differential equations, spline functions, function approximation, the definition of a stochastic process, and inference from so-called inadequate and inaccurate data. Section 1 states a metatheorem about why and when reproducing kernel Hilbert spaces RKHS arise. Section 2 formulates general approximation problems in Hilbert space and indicates why they need to be viewed probabilistically. Section 3 outlines the motivation for control theorizing away filtering problems. Section 4 outlines a filtering theory for Hilbert space indexed time series. Related work is mentioned in Section 5. Author
- Statistics and Probability