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

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)

Document Details

Document Type
Technical Report
Publication Date
May 14, 1971
Accession Number
AD0728991

Entities

People

  • Emanuel Parzen

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Control Theory
  • Differential Equations
  • Equations
  • Filtration
  • Hilbert Space
  • Integral Equations
  • Partial Differential Equations
  • Stochastic Processes

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Theoretical Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • Space