Sampling Designs for Estimating Integrals of Stochastic rocesses Using Quadratic Mean Derivatives

Abstract

The problem of estimating the integral of a stochastic process by linear estimators based on observations of the process and its existing quadratic mean (q.m.) derivatives at a finite number of sampling points is considered. The process is assumed to have exactly K q.m. derivatives, K=O, 1,2, ..... The asymptotic performance of optimal-coefficient estimators that depend on an inverse matrix is determined for regular sampling designs under slightly different assumptions than those in Sacks and Ylvisaker (1970). Simple- coefficient estimators based on a trapezoidal rule with a correction term that depends on the q.m. derivatives of the process at all sampling points of a regular design are introduced. Their asymptotic performance is identical to that of the optimal-coefficient estimators. Keywords: Linear equations, Stochastic processes, Integrals.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1990
Accession Number
ADA225961

Entities

People

  • Karim Benhenni
  • Stamatis Cambanis

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Classification
  • Covariance
  • Data Science
  • Differential Equations
  • Equations
  • Estimators
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • Integrals
  • North Carolina
  • Sampling
  • Security
  • Stationary Processes
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Quantum Chemistry
  • Statistical inference.