TY - JOUR

T1 - The debiased Whittle likelihood

AU - Sykulski, Adam M.

AU - Olhede, Sofia C.

AU - Guillaumin, Arthur P.

AU - Lilly, Jonathan M.

AU - Early, Jeffrey J.

N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version Adam M Sykulski, Sofia C Olhede, Arthur P Guillaumin, Jonathan M Lilly, Jeffrey J Early, The debiased Whittle likelihood, Biometrika, Volume 106, Issue 2, June 2019, Pages 251–266, is available online at: https://academic.oup.com/biomet/article/106/2/251/5318578

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

KW - Parameter estimation

KW - Pseudolikelihood

KW - Fast Fourier Transform

KW - Frequency Domain

KW - Computational efficiency

U2 - 10.1093/biomet/asy071

DO - 10.1093/biomet/asy071

M3 - Journal article

VL - 106

SP - 251

EP - 266

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -