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- J M Angulo, M C Bueso
- 2001

SUMMARY The problem of estimating a multivariate spatial random process from observations obtained by sampling a related multivariate spatial random process is considered. A method based on additive perturbation of the variables of interest is proposed for the assignment of degrees of relative importance to the variables and/or locations of interest in the… (More)

- M. D. Ruiz-Medina, J. M. Angulo, V. V. Anh, MARCEL DEKKER
- 2003

Using the theory of generalized random fields on fractional Sobolev spaces on bounded domains, and the concept of dual generalized random field, this paper introduces a class of random fields with fractional-order pure point spectra. The covariance factorization of an a-generalized random field having a dual is established, leading to a white-noise… (More)

- M. C. Bueso, J. M. Angulo, J. Cruz-Sanjulián, J. L. Garcı́a-Aróstegui
- 1999

3 The problem of spatial sampling design for estimating a multivariate random field from information obtained by sampling related variables is considered. A formulation assigning different degrees of importance to the variables and locations involved is introduced. Adopting an entropy-based approach, an objective function is defined as a linear combination… (More)

A new methodology is introduced for spatial sampling design when the variable of interest cannot be directly observed, but information on it can be obtained by sampling a related variable, and estimation of the underlying model is required. in the case where a model for the involved variables is given. However, in some cases a predetermined structure… (More)

In a previous paper (Environ. Ecol. Stat. 5 (1998) 29.) we presented an entropy-based approach to spatial sampling design in a state-space model framework. We now address the problem of sensitivity of optimal designs with respect to the configuration of the set of potential observation sites considered, as well as to the model specifications. The latter… (More)

The least-squares linear inverse estimation problem for random fields is studied in a fractional generalized framework. First, the second-order regularity properties of the random fields involved in this problem are analysed in terms of the fractional Sobolev norms. Second, the incorporation of prior information in the form of a fractional stochastic model,… (More)

In this paper, a class of spatio-temporal processes with first-order autoregressive temporal structure and functional spatio-temporal interaction is introduced. The spatial second-order regularity is allowed to change over time and is characterized in terms of fractional Sobolev spaces. The associated filtering problem is considered, assuming that… (More)

Using the geometric properties of Sobolev spaces of integer order and a duality condition, the covariance operators of a generalized random field and its dual can be factorized. Via this covari-ance factorization, a representation of the generalized random field is obtained as a stochastic equation driven by generalized white noise. This stochastic equation… (More)