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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| Language: | English |
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Wiley
2017-01-01
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| 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. |
| format | Article |
| id | doaj-art-e55629670c3e4092ba0700e47ed6d5de |
| institution | OA Journals |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| 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 |