Fixed-domain asymptotic properties of tapered maximum likelihood estimators

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 Mat\'ern 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 Mat\'ern model.Comment: Published in at http://dx.doi.org/10.1214/08-AOS676 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Note on symmetric BCJ numerator

We present an algorithm that leads to BCJ numerators satisfying manifestly the three properties proposed by Broedel and Carrasco in [35]. We explicitly calculate the numerators at 4, 5 and 6-points and show that the relabeling property is generically satisfied.Comment: 14 pages, typo in eq.(4.1)is correcte