Fixed-domain asymptotic properties of tapered maximum likelihood estimators

By Juan Du, Hao Zhang, V. Mandrekar. 2009

151 citations recorded by the source corpus.

When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. Under the assumption that data are collected along a line in a bounded region, we investigate how the tapering affects the asymptotic efficiency of the maximum likelihood estimator (MLE) for the microergodic parameter in the Matern covariance function by establishing the fixed-domain asymptotic distribution of the exact MLE and that of the tapered MLE. Our results imply that, under some conditions on the taper, the tapered MLE is asymptotically as efficient as the true MLE for the microergodic parameter in the Matern model.

Subfields: Economics and Econometrics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/688ae2db5caaf0134c22e64c352e8853a44678cb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Matérn Cross-Covariance Functions for Multivariate Random Fields (2010, background): “Du, Zhang, and Mandrekar (2009) study the corresponding asymptotic distribution, and extend results of Ying (1991), who showed that if ν = 12 then either a or σ 2 can be fixed arbitrarily and the composite quantity can still be estimated consistently and efficiently.”
On fixed-domain asymptotics and covariance tapering in Gaussian random field models (2011, background): “[5] obtained similar results for the tapered MLE (obtained by maximizing (5) with respect to both α1 and σ1).”
Tapered Covariance: Bayesian Estimation and Asymptotics (2012, background): “Here, like Kaufman (2006), Kaufman, Schervish, and Nychka (2008), Zhang and Du (2008), and Du, Zhang, and Mandrekar (2009), we study the use of tapering for parameter estimation.”
A General Framework for Vecchia Approximations of Gaussian Processes (2017, background): “These include approaches leading to sparse co-variance matrices (Furrer et al., 2006; Kaufman et al., 2008; Du et al., 2009), sparse inverse 2 A general Vecchia approach 2.1 Noisy observations of a Gaussian process Let { y ( s ) : s ∈ D} , or y ( · ), be a process of interest on a continuous (i.e.,…”
Penalized maximum likelihood estimation and variable selection in geostatistics (2011, methodology): “In addition, we explore covariance tapering, which further reduces computational cost by replacing the exact covariance matrix with a sparse one [4, 9, 12].”
On the consistent separation of scale and variance for Gaussian random fields (2009, methodology): “Recent work by Kaufman, Schervish and Nychka [20] and Du, Zhang and Mandrekar [12] studies maximum likelihood estimates of σ 2α2ν using a tapered Matérn autocovariance when d ≤ 3.”
Statistical Properties of Covariance Tapers (2013, result): “Indeed, Kaufman, Schervish, and Nychka (2008); Du, Zhang, and Mandrekar (2009); Kaufman and Shaby (2011); and Wang and Loh (2011) gave limited results in this regard for tapering as applied to Matérn acfs.”
Classes of compactly supported covariance functions for multivariate random fields (2015, methodology): “This class of covariance functions has been used repeatedly in applications involving so-called tapered likelihoods (Furrer et al. 2006; Kaufman et al. 2008; Du et al. 2009).”
Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets (2014, methodology): “Methods exploiting sparse covariance structures include covariance tapering methods (see, e.g., Furrer et al. 2006; Kaufman et al. 2008; Du et al. 2009) or likelihood approximations using Markov random fields (e.”