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Spatial sampling design for prediction with estimated parameters
 Journal of Agricultural Biological and Environmental Statistics
, 2006
"... We study spatial sampling design for prediction of stationary isotropic Gaussian processes with estimated parameters of the covariance function. The key issue is how to incorporate the parameter uncertainty into design criteria to correctly represent the uncertainty in prediction. Several possible ..."
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Cited by 13 (1 self)
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We study spatial sampling design for prediction of stationary isotropic Gaussian processes with estimated parameters of the covariance function. The key issue is how to incorporate the parameter uncertainty into design criteria to correctly represent the uncertainty in prediction. Several possible design criteria are discussed that incorporate the parameter uncertainty. A simulated annealing algorithm is employed to search for the optimal design of small sample size and a twostep algorithm is proposed for moderately large sample sizes. Simulation results are presented for the Matérn class of covariance functions. An example of redesigning the air monitoring network in EPA Region 5 for monitoring sulfur dioxide is given to illustrate the possible differences our proposed design criterion can make in practice. Key Words: Fisher information matrix; Geostatistics; Kriging; Kullback divergence; Optimization; Simulated annealing.
Optimal Designs for Weighted Approximation and Integration of Stochastic Processes on [0, ∞)
 J. Complexity
, 2002
"... We study minimal errors and optimal designs for weighted L 2 approximation and weighted integration of Gaussian stochastic processes X defined on the halfline [0; 1). ..."
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Cited by 6 (3 self)
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We study minimal errors and optimal designs for weighted L 2 approximation and weighted integration of Gaussian stochastic processes X defined on the halfline [0; 1).
Uniform Reconstruction of Gaussian Processes
, 1995
"... We consider a Gaussian process X with smoothness comparable to the Brownian motion. We analyze reconstructions of X which are based on observations at finitely many points. For each realization of X the error is defined in a weighted supremum norm; the overall error of a reconstruction is defined as ..."
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Cited by 3 (1 self)
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We consider a Gaussian process X with smoothness comparable to the Brownian motion. We analyze reconstructions of X which are based on observations at finitely many points. For each realization of X the error is defined in a weighted supremum norm; the overall error of a reconstruction is defined as the pth moment of this norm. We determine the rate of the minimal errors and provide different reconstruction methods which perform asymptotically optimal. In particular, we show that linear interpolation at the quantiles of a certain density is asymptotically optimal.
ON ESTIMATION OF REGULARITY FOR GAUSSIAN PROCESSES
"... Abstract. We consider a real Gaussian process X with unknown smoothness r 0 where r 0 is a nonnegative integer and the meansquare derivative X (r0) is supposed to be locally stationary of index β 0. From n + 1 equidistant observations, we propose and study an estimator of (r 0,β 0) based on results ..."
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Abstract. We consider a real Gaussian process X with unknown smoothness r 0 where r 0 is a nonnegative integer and the meansquare derivative X (r0) is supposed to be locally stationary of index β 0. From n + 1 equidistant observations, we propose and study an estimator of (r 0,β 0) based on results for quadratic variations of the underlying process. Various numerical studies of these estimators derive their properties for finite sample size and different types of processes, and are also completed by two examples of application to real data. hal00750409, version 1 9 Nov 2012 1.