Minimum Contrast Estimation for Spectral Densities of Stationary Processes
提出用参数族逼近真实谱密度，通过最小化对比函数得到参数估计量，并给出其渐近分布和有效性条件，适用于时间序列谱分析。
SUMMARY Let {z(n)} be a stationary process with mean zero and true spectral density g(λ). In this paper we approximate g(λ) by a parametric family f θ(λ) and propose a minimum contrast estimator θ^ which minimizes D(fθ,g^N)=∫−ππK{fθ(λ)/g^N(λ)}dλ with respect to θ, where K(.) is an appropriate function and ĝ N(λ) is a nonparametric spectral estimator of g(λ). We give the asymptotic distribution of θ^ and sufficient conditions such that θ^ is asymptotically efficient. Also, we show that for various spectra f θ(λ), if we choose K(.) in D(f θ, g) appropriately, we obtain a non-iterative efficient estimator of θ in explicit form.