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

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 me...

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Main Author: K. Perera
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2017/6219149
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author K. Perera
author_facet K. Perera
author_sort K. Perera
collection DOAJ
description 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.
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spelling doaj-art-e55629670c3e4092ba0700e47ed6d5de2025-08-20T02:21:18ZengWileyJournal of Probability and Statistics1687-952X1687-95382017-01-01201710.1155/2017/62191496219149Estimation of the Parameters of a Chirp Type Model with Stationary ResidualsK. Perera0Department of Engineering Mathematics, Faculty of Engineering, University of Peradeniya, Peradeniya, Sri LankaLet 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.http://dx.doi.org/10.1155/2017/6219149
spellingShingle K. Perera
Estimation of the Parameters of a Chirp Type Model with Stationary Residuals
Journal of Probability and Statistics
title Estimation of the Parameters of a Chirp Type Model with Stationary Residuals
title_full Estimation of the Parameters of a Chirp Type Model with Stationary Residuals
title_fullStr Estimation of the Parameters of a Chirp Type Model with Stationary Residuals
title_full_unstemmed Estimation of the Parameters of a Chirp Type Model with Stationary Residuals
title_short Estimation of the Parameters of a Chirp Type Model with Stationary Residuals
title_sort estimation of the parameters of a chirp type model with stationary residuals
url http://dx.doi.org/10.1155/2017/6219149
work_keys_str_mv AT kperera estimationoftheparametersofachirptypemodelwithstationaryresiduals