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摘要翻译：
研究了一个季节持续平稳随机过程的频谱参数估计问题。对于与频率零点以外的谱中极点相关的季节性持续性，提出了一种新的Whittle型似然，它明确地确认了极点的位置。该Whittle似然性是周期图在选定的频率网格上的分布的大样本近似，并通过与解调相结合的逆离散傅里叶变换的线性变换构成对数据的时域似然性的近似。新的似然性很容易计算，而且正如我们将演示的那样，它具有良好的、但非标准的性质。研究了所提出的似然估计的渐近性态；特别地，建立了谱极点位置估计量的$N$-相合性。给出了分数和观测Fisher信息的大样本渐近分布，以及相应的极大似然估计的分布。研究了似然近似的小样本性质，证明了似然近似比以前提出的方法具有更好的性能，并与已发展的分布近似相一致。
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英文标题：
《Non-Regular Likelihood Inference for Seasonally Persistent Processes》
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作者：
Emma J. McCoy, Sofia C. Olhede and David A. Stephens
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
The estimation of parameters in the frequency spectrum of a seasonally persistent stationary stochastic process is addressed. For seasonal persistence associated with a pole in the spectrum located away from frequency zero, a new Whittle-type likelihood is developed that explicitly acknowledges the location of the pole. This Whittle likelihood is a large sample approximation to the distribution of the periodogram over a chosen grid of frequencies, and constitutes an approximation to the time-domain likelihood of the data, via the linear transformation of an inverse discrete Fourier transform combined with a demodulation. The new likelihood is straightforward to compute, and as will be demonstrated has good, yet non-standard, properties. The asymptotic behaviour of the proposed likelihood estimators is studied; in particular, $N$-consistency of the estimator of the spectral pole location is established. Large finite sample and asymptotic distributions of the score and observed Fisher information are given, and the corresponding distributions of the maximum likelihood estimators are deduced. A study of the small sample properties of the likelihood approximation is provided, and its superior performance to previously suggested methods is shown, as well as agreement with the developed distributional approximations.
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PDF链接：
https://arxiv.org/pdf/709.0139
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