Spatial Field Reconstruction of Non-Gaussian Random Fields: The Tukey G-and-H Random Process

37 Pages Posted: 27 Apr 2018

See all articles by Sai Ganesh Nagarajan

Sai Ganesh Nagarajan

Singapore University of Technology and Design (SUTD)

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Ido Nevat

Heriot-Watt University - Department of Actuarial Mathematics and Statistics

Date Written: April 9, 2018

Abstract

A new class of models for non-Gaussian spatial random fields is developed for spatial field reconstruction in environmental and sensory network monitoring. The developed family of models utilises a class of transformation functions known as the Tukey g-and-h transformation to create a new class of warped spatial Gaussian process model which can support various desirable features such as flexible marginal distributions, which can be skewed and/or heavy-tailed. The resulting model is widely applicable for a wide range of spatial field reconstruction applications. To utilise the model for such applications in practice, we first need to derive the statistical properties of the new family of Tukey g-and-h random fields. We are then able to derive five different objectives to perform spatial field reconstruction. These include the Minimum Mean Squared Error (MMSE), Maximum A-Posteirori (MAP) and the Spatial-Best Linear Unbiased (S-BLUE) estimators as well as the Spatial Regional and Level Exceedance estimators. Extensive simulation results and real data examples show the benefits of using the Tukey g-and-h transformation as opposed to standard Gaussian spatial random fields as is classically utilised.

Keywords: Tukey Process, Co-Skewness, Co-Kurtosis, Non-Gaussian Spatial Process, Spatial Field Reconstruction

Suggested Citation

Nagarajan, Sai Ganesh and Peters, Gareth and Nevat, Ido, Spatial Field Reconstruction of Non-Gaussian Random Fields: The Tukey G-and-H Random Process (April 9, 2018). Available at SSRN: https://ssrn.com/abstract=3159687 or http://dx.doi.org/10.2139/ssrn.3159687

Sai Ganesh Nagarajan

Singapore University of Technology and Design (SUTD) ( email )

20 Dover Drive
Singapore, 138682
Singapore

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Ido Nevat

Heriot-Watt University - Department of Actuarial Mathematics and Statistics ( email )

Edinburgh, Scotland EH14 4AS
United Kingdom

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