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: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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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| ISSN: | 1687-952X 1687-9538 |