Discrete-Time Spectral Estimation of Continuous-Time Processes - the Orthogonal Series Method (Spectral Estimation by Orthogonal Series),

Abstract

Let X = (X(t), - infinity < t < infinity) be a stationary time series with spectral density function phi(lambda). Let (t sub n) be a stationary poisson point process on (- infinity, infinity), independent of X. The existence of consistent estimates of phi(lambda) based on the discrete-time observations (X(t sub n)), when the actual sampling instants (t sub n) are not known, has been an open question. Using an orthogonal series method, a class of spectral estimates is considered and its uniform and integratedly uniform consistency in quadratic mean is established. The rates of convergence are determined and compared with those of the kernel-type estimates based on the observations (X(t sub n), t sub n). (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1979
Accession Number
ADA070641

Entities

People

  • Elias Masry

Organizations

  • University of California, San Diego

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Consistency
  • Convergence
  • Data Science
  • Fluid Mechanics
  • Information Science
  • Laguerre Functions
  • Military Research
  • Observation
  • Order Statistics
  • Probability
  • Random Variables
  • Sampling
  • Sequences
  • Stationary
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.