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

Abstract EN

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.