Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes
Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes
复制标题
高斯局部平稳过程的非参数拟极大似然估计
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
W. Polonik
中科院分区：
文献类型：
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作者：
R. Dahlhaus;W. Polonik
本文讨论高斯局部平稳过程的非参数极大似然估计。我们的非参数极大似然估计是通过最小化一类函数的频域似然来构造的。研究了所得估计量的渐近性质。结果取决于丰富的功能类。筛估计和整体估计。我们的研究结果适用于，特别是形状约束下的估计。作为一个例子，自回归模型拟合单调方差函数进行了详细讨论，包括算法的考虑。一个关键的技术工具是由函数索引的时变经验谱过程。对于这一过程，得到了一个Bernstein型指数不等式和一个中心极限定理。经验谱过程的这些结果是独立的利益。
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior of the resulting estimator is studied. The results depend on the richness of the class of functions. Both sieve estimation and global estimation are considered. Our results apply, in particular, to estimation under shape constraints. As an example, autoregressive model fitting with a monotonic variance function is discussed in detail, including algorithmic considerations. A key technical tool is the time-varying empirical spectral process indexed by functions. For this process, a Bernstein-type exponential inequality and a central limit theorem are derived. These results for empirical spectral processes are of independent interest.