A frequency domain empirical likelihood method for irregularly spaced spatial data
不规则间距空间数据的频域经验似然方法AI 解读 ↓
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不规则间距空间数据的频域经验似然方法
- 研究问题
- 面对不规则间距空间观测引起的傅里叶正交性缺失与周期图偏差，如何对谱估计方程定义的协方差参数进行推断？
- 方法与思路
- 作者构造考虑非正交性与周期图偏差的空间频域经验似然，并研究缩放后对数似然比的极限分布及数值表现。
- 材料陈述的贡献
- 摘要称，缩放统计量具有卡方极限，可构造渐近正确的非参数置信域与检验，且无需显式估计估计量标准误。
- 阅读关注点
- 应核对空间渐近框架、采样密度条件、周期图偏差处理，以及似然比缩放因子的确定和数值研究的有限样本表现。
- 阅读边界
- 仅据版本未注明的OpenAlex索引摘要；空间依赖条件和缩放细节未说明，渐近分布无关性不等于有限样本精确性。
原文摘要
This paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain empirical likelihood (FDEL) methodology for time series (on a regular grid), the formulation of the spatial FDEL needs special care due to lack of the usual orthogonality properties of the discrete Fourier transform for irregularly spaced data and due to presence of nontrivial bias in the periodogram under different spatial asymptotic structures. A spatial FDEL is formulated in the paper taking into account the effects of these factors. The main results of the paper show that Wilks’ phenomenon holds for a scaled version of the logarithm of the proposed empirical likelihood ratio statistic in the sense that it is asymptotically distribution-free and has a chi-squared limit. As a result, the proposed spatial FDEL method can be used to build nonparametric, asymptotically correct confidence regions and tests for covariance parameters that are defined through spectral estimating equations, for irregularly spaced spatial data. In comparison to the more common studentization approach, a major advantage of our method is that it does not require explicit estimation of the standard error of an estimator, which is itself a very difficult problem as the asymptotic variances of many common estimators depend on intricate interactions among several population quantities, including the spectral density of the spatial process, the spatial sampling density and the spatial asymptotic structure. Results from a numerical study are also reported to illustrate the methodology and its finite sample properties.