Estimation of spectral densities with multiplicative parameter (Q1415512)

Let \(\{Y(t)\), \(t\in[0,T]^n\}\) be a stationary random field with zero mean and spectral density \(f(\lambda)=\eta g(\lambda;\theta)\), where \(\eta\) and \(\theta\) are unknown parameters. The authors propose a two-step method for estimating the parameters. First, a minimum contrast estimator for \(\theta\) is constructed and then it is used for estimating \(\eta\). The consistency and asymptotic normality of the estimators are proved.