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Title: Fast and efficient parameter estimation in time series and random fields Authors:  Adam Sykulski - Lancaster University (United Kingdom) [presenting]
Arthur Guillaumin - University College London (United Kingdom)
Sofia Olhede - EPFL (Switzerland)
Abstract: Balancing computational and statistical efficiency is a modern challenge of statistical inference. We discuss new methods for parameter estimation in time series and random fields which addresses this very challenge. Specifically, we propose a class of new pseudo-likelihood estimators which are order $N\log N$ to compute, and yield parameter estimates with optimal $\sqrt{N}$ convergence under weaker assumptions than alternative methods. The procedure is inspired from the Whittle likelihood, and as thus is based in the frequency domain, but we make important bias corrections to vastly improve performance. We also extend the procedure to include missing data and irregular spatial shapes, as well as non-linear, non-stationary and anisotropic stochastic processes. We demonstrate the applicability of our techniques to massive datasets across oceanography and the geosciences.