The debiased Whittle likelihood
The debiased Whittle likelihood
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DOI：
10.1093/biomet/asy071
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发表时间：
2019-02
期刊：
影响因子：
2.7
通讯作者：
A. Sykulski;S. Olhede;Arthur Guillaumin;J. Lilly;J. Early
中科院分区：
文献类型：
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作者：
A. Sykulski;S. Olhede;Arthur Guillaumin;J. Lilly;J. Early
Whittle似然是一种广泛使用且计算效率高的伪似然。然而，它是已知的，以产生偏置的参数估计与有限的样本大小的大类模型。提出了一种二阶平稳随机过程的去偏Whittle估计的方法。去偏的Whittle似然可以在与标准Whittle方法相同的O（n log n）操作中计算。我们证明了我们的方法在模拟研究中的上级性能，并在应用到一个大规模的海洋数据集，在这两种情况下，去偏的方法减少偏差高达两个数量级，实现估计接近的确切的最大似然，在一小部分的计算成本。我们证明了该方法产生的估计是一致的，在最佳收敛速度为n（-1/2）的高斯过程和某些类的非高斯或非线性过程。这是在比标准理论更弱的假设下建立的，特别是功率谱密度不需要在频率上连续。我们描述了该方法如何可以很容易地结合标准的偏差减少方法，如锥形和差分，以进一步减少参数估计的偏差。
The Whittle likelihood is a widely used and computationally efficient pseudolikelihood. However, it is known to produce biased parameter estimates with finite sample sizes for large classes of models. We propose a method for debiasing Whittle estimates for second-order stationary stochastic processes. The debiased Whittle likelihood can be computed in the same O(n log n) operations as the standard Whittle approach. We demonstrate the superior performance of our method in simulation studies and in application to a large-scale oceanographic dataset, where in both cases the debiased approach reduces bias by up to two orders of magnitude, achieving estimates that are close to those of the exact maximum likelihood, at a fraction of the computational cost. We prove that the method yields estimates that are consistent at an optimal convergence rate of n(-1/2) for Gaussian processes and for certain classes of non-Gaussian or nonlinear processes. This is established under weaker assumptions than in the standard theory, and in particular the power spectral density is not required to be continuous in frequency. We describe how the method can be readily combined with standard methods of bias reduction, such as tapering and differencing, to further reduce bias in parameter estimates.