| 摘要: |
| 基于多维网格上大规模空间数据的似然方法往往存在计算困难的问题.当样本量较大时, 因涉及协方差矩阵的求逆, 似然方法计算复杂度较高.借助观测数据的周期图而建立的Whittle似然函数,可用于近似精确似然函数. 利用快速Fourier变换,Whittle似然方法计算效率较高.然而,Whittle似然方法会产生有偏估计. 融合核函数加权与纠偏的思想,在研究周期图均值的基础上, 提出了局部纠偏Whittle似然的推断方法,并证明了局部纠偏Whittle似然估计具有渐近正态性. 模拟结果表明: 相比局部Whittle似然方法, 该方法在谱密度推断中有更好的表现. |
| 关键词: 局部Whittle似然 纠偏 谱密度 周期图 空间统计 |
| DOI：10.3969/J.ISSN.1000-5137.2022.03.012 |
| 分类号:O212 |
| 基金项目:国家自然科学基金(11971116) |
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| Local de-biased Whittle likelihood method for spatial lattice data |
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YAO Kaili, ZHU Bingfan, LI Yan, ZHANG Shibin
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Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| The likelihood method based on large-scale spatial data on multi-dimensional grids is often encountered with the problem of computational difficulty. When the sample size is large, the computational complexity of likelihood method is high, for it involves the inversion of covariance matrix. The Whittle likelihood funtion, which is set up from the periodogram of the observations, provides a good approximation to the true likelihood. Using the fast Fourier transform, the computation in Whittle likelihood method is very efficient. However, this approach may produce biased estimators. Combining the ideas of kernel-function-weighting and de-biasing, a local de-biased Whittle likelihood method, which is established based on the expectation of periodogram, has been proposed. It is proved that the estimator minimizing the local de-biased Whittle likelihood, achieves the asymptotic normality. The simulation study shows the proposed approach outperforms the local Whittle likelihood in statistical inference for the spectral density. |
| Key words: local Whittle likelihood de-biasing spectral density periodogram spatial statistics |
