Accession Number : AD0728991

Title :   On the Equivalence Among Time Series Parameter Estimation, Approximation Theory, and Control Theory.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Parzen,Emanuel

Report Date : 14 MAY 1971

Pagination or Media Count : 23

Abstract : 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)

Descriptors :   (*TIME SERIES ANALYSIS, MATHEMATICAL PREDICTION), (*CONTROL SYSTEMS, MATHEMATICAL MODELS), (*APPROXIMATION(MATHEMATICS), FUNCTIONS), PARTIAL DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, STOCHASTIC PROCESSES, INFORMATION THEORY, HILBERT SPACE, INTERPOLATION, INTEGRATION

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE