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Spectral and Probability Density Estimation From Irregularly Observed Data

  • Elias Masry
Part of the Lecture Notes in Statistics book series (LNS, volume 25)

Abstract

Let X = {X(t), − ∞ < t < ∞} be a stationary stochastic process with univariate probability density f(x), covariance function R(t), and spectral density φ(λ). The nonparametric estimation of f, R, and φ on the basis of irregularly-spaced observations \(\left\{ {{\text{X}}\left( {{\text{t}}_{\text{k}} } \right){\text{,t}}_{\text{k}} } \right\}_{{\text{k = 1}}}^{\text{n}}\) is considered. The sampling schemes {tk} which allow the consistent estimation of f, R, and φ, as the sample size n → ∞, are identified and the asymptotic statistical properties of the corresponding estimates \({\hat f_n}\left( x \right),{\hat f_n}\left( t \right)\), and \(\hat \varphi _{\text{n}} \left( \lambda \right)\) are presented.

Keywords

Point Process Sampling Instant Stationary Stochastic Process Probability Density Estimation Random Sampling Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Elias Masry
    • 1
  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaSan Diego, La JollaUSA

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