Nonparametric spatial prediction under stochastic sampling design

Menezes, Raquel; García-Soidán, Pilar; Ferreira, Célia

doi:10.1080/10485250903094294

Cited by 16 publications

(13 citation statements)

References 24 publications

(13 reference statements)

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“…Later, Dabo-Niang and Yao [6] were interested in the kernel regression estimation and prediction of continuously indexed random fields. In [11], nonparametric kernel prediction was considered for spatial stochastic processes when a stochastic sampling design is assumed for the selection of random locations. A main difference between them is that the last is based on a kernel that controls the distance between sites contrary to the others, which deal with a kernel on the values of the field.…”

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confidence: 99%

A new spatial regression estimator in the multivariate context

Dabo‐Niang

Ternynck

Yao

2015

Comptes Rendus. Mathématique

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mentioning

confidence: 99%

A new spatial regression estimator in the multivariate context

Dabo‐Niang

Ternynck

Yao

2015

Comptes Rendus. Mathématique

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“…These procedures would yield optimal bandwidths (Liu, ), although they would be unknown in practice due to their dependence on the underlying distribution. Hence, we explore other alternatives for the selection of the bandwidth parameters, more easily attainable for a given data set, such as those based on the cross‐validation methods (Hall et al, ; Menezes et al, ) or on the balloon estimation (Terrell & Scott, ; García‐Soidán & Menezes, ).…”

Section: Methodsmentioning

confidence: 99%

“…For such a situation, two kernel‐based procedures have been applied, which are mainly dependent on whether the value of the random process at the target location is needed. When this observation is not required, as in the derivation of a kernel predictor at a specific site (Menezes et al, ), the kernel approach can be designed so as to account for the lags between the target site and the sampled locations. This way of proceeding offers the advantage that it can be applied to random processes departing from the stationarity condition.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric construction of probability maps under local stationarity

García-Soidán

Menezes

2017

Environmetrics

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The environmental contamination risk can be evaluated in a specific area by approximating the probability that the pollutant under study exceeds a critical value. This issue requires the estimation of the distribution function involved, which can be addressed by applying the indicator kriging methodology or by approximating the sill of the variogram of the underlying indicator process. These approaches demand an appropriate characterization of the indicator variogram, which in turn requires a previous specification of the trend function, if the latter is suspected to be nonconstant. Because accuracy of the results will be strongly dependent on the adequate approximation of both functions, we suggest proceeding in a different way to avoid these requirements. Thus, in this paper, two kernel‐type estimators are proposed, on the basis of first approximating the distribution at the sampled sites and then obtaining a weighted average of the resulting values, to derive a valid estimator at each (sampled or unsampled) location. Consistency of the kernel approaches is proved under rather general conditions, such as local stationarity and the existence of derivatives up to the second order of the distribution function. Numerical studies have been carried out to illustrate the performance of our proposals when compared to those procedures requiring the approximation of the indicator variogram. In a final step, the kernel‐type estimation of the distribution function has been applied to map the risk of contamination by arsenic in the Central Region of Portugal. With this aim, biomonitoring data of arsenic concentrations were used to detect those zones with higher risk of arsenic accumulation, which is mainly located on the northern part of the region.

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“…In the univariate setting, the nonparametric prediction of variable Z 1 at an unsampled location s can be addressed by only considering the data collected for the target variable, together with the application of the methodology developed in [25], yieldinĝ…”

Section: Nonparametric Predictormentioning

confidence: 99%

“…To avoid the aforementioned problems, the current research provides a nonparametric alternative for prediction in this setting, derived by extending the univariate approach without covariables that was proposed in [25]. The current work is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Use of Correlated Data for Nonparametric Prediction of a Spatial Target Variable

García-Soidán

Cotos-Yáñez

2020

Mathematics

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The kriging methodology can be applied to predict the value of a spatial variable at an unsampled location, from the available spatial data. Furthermore, additional information from secondary variables, correlated with the target one, can be included in the resulting predictor by using the cokriging techniques. The latter procedures require a previous specification of the multivariate dependence structure, difficult to characterize in practice in an appropriate way. To simplify this task, the current work introduces a nonparametric kernel approach for prediction, which satisfies good properties, such as asymptotic unbiasedness or the convergence to zero of the mean squared prediction error. The selection of the bandwidth parameters involved is also addressed, as well as the estimation of the remaining unknown terms in the kernel predictor. The performance of the new methodology is illustrated through numerical studies with simulated data, carried out in different scenarios. In addition, the proposed nonparametric approach is applied to predict the concentrations of a pollutant that represents a risk to human health, the cadmium, in the floodplain of the Meuse river (Netherlands), by incorporating the lead level as an auxiliary variable.

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Nonparametric spatial prediction under stochastic sampling design

Cited by 16 publications

References 24 publications

A new spatial regression estimator in the multivariate context

A new spatial regression estimator in the multivariate context

Nonparametric construction of probability maps under local stationarity

Use of Correlated Data for Nonparametric Prediction of a Spatial Target Variable

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