Bernstein polynomial estimation of a spectral density
Bernstein polynomial estimation of a spectral density
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DOI：
10.1111/j.1467-9892.2005.00465.x
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发表时间：
2006-03
影响因子：
0.9
通讯作者：
Yoshihide Kakizawa
中科院分区：
文献类型：
--
作者：
Yoshihide Kakizawa
抽象的。考虑了伯恩斯坦多项式在平稳过程谱密度估计中的应用。由此产生的估计量可以被解释为m个点处的（Daniell）核谱密度估计量的凸组合，其系数是二项分布bin（m-1，|λ|/π），λ ∈ π [− π，π]是进行谱密度估计的频率。在次数为m的条件下，研究了几个渐近性质.我们还讨论了度m的数据驱动选择方法。为了与普通核方法进行比较，蒙特卡罗模拟说明了我们的方法，并检查其性能在小样本。
Abstract. We consider an application of Bernstein polynomials for estimating a spectral density of a stationary process. The resulting estimator can be interpreted as a convex combination of the (Daniell) kernel spectral density estimators at m points, the coefficients of which are probabilities of the binomial distribution bin(m − 1, |λ|/π), λ ∈ Π ≡ [−π, π] being the frequency where the spectral density estimation is made. Several asymptotic properties are investigated under conditions of the degree m. We also discuss methods of data‐driven choice of the degree m. For a comparison with the ordinary kernel method, a Monte Carlo simulation illustrates our methodology and examines its performance in small sample.