Spectral and Probability Density Estimation From Irregularly Observed Data

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


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.


Point Process Sampling Instant Stationary Stochastic Process Probability Density Estimation Random Sampling Scheme 
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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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