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Estimation of the Parameters of a Chirp Type Model with Stationary Residuals.

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Title: Estimation of the Parameters of a Chirp Type Model with Stationary Residuals.
Authors: Perera, K.1
Source: Journal of Probability & Statistics. 2/9/2017, p1-14. 14p.
Subjects: Chirp modulation, Statistical maps, Statistical models, Approximation theory, Least squares
Abstract: Let Xn1,…,Xnn be the observations from a chirp type statistical model Xnt, Xnt=Acos⁡ (ωt+Δ/nt2)+Bsin⁡ ωt+Δ/nt2+ϵt, where ϵt is a stationary noise. We consider a method of estimation of parameters, A, B, ω, Δ, and ν, (where ν is the variance of ϵt’s) which is basically an approximate least-squares method. The main advantage of the proposed approach is that no assumptions are required. We make use of the three theorems which were established associated with the kernel ∑t=1neiut+vt2 and then use them to prove, under certain conditions, the consistency of the estimators. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Probability & Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Estimation of the Parameters of a Chirp Type Model with Stationary Residuals.
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  Data: <searchLink fieldCode="DE" term="%22Chirp+modulation%22">Chirp modulation</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+maps%22">Statistical maps</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Least+squares%22">Least squares</searchLink>
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  Data: Let Xn1,…,Xnn be the observations from a chirp type statistical model Xnt, Xnt=Acos⁡ (ωt+Δ/nt2)+Bsin⁡ ωt+Δ/nt2+ϵt, where ϵt is a stationary noise. We consider a method of estimation of parameters, A, B, ω, Δ, and ν, (where ν is the variance of ϵt’s) which is basically an approximate least-squares method. The main advantage of the proposed approach is that no assumptions are required. We make use of the three theorems which were established associated with the kernel ∑t=1neiut+vt2 and then use them to prove, under certain conditions, the consistency of the estimators. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Probability & Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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    Identifiers:
      – Type: doi
        Value: 10.1155/2017/6219149
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 14
        StartPage: 1
    Subjects:
      – SubjectFull: Chirp modulation
        Type: general
      – SubjectFull: Statistical maps
        Type: general
      – SubjectFull: Statistical models
        Type: general
      – SubjectFull: Approximation theory
        Type: general
      – SubjectFull: Least squares
        Type: general
    Titles:
      – TitleFull: Estimation of the Parameters of a Chirp Type Model with Stationary Residuals.
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            NameFull: Perera, K.
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            – D: 09
              M: 02
              Text: 2/9/2017
              Type: published
              Y: 2017
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            – TitleFull: Journal of Probability & Statistics
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