Prediction of Spatial Cumulative Distribution Functions Using Subsampling

Lahiri, Soumendra N.; Kaiser, Mark J.; Cressie, Noel; Hsu, Nan‐Jung

doi:10.2307/2669680

Cited by 45 publications

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“…We assume that the sampling region R n is obtained by "inflating" the set R 0 by the scaling factor λ n (cf. Lahiri et al [22]), that is,…”

Section: Sampling Regionsmentioning

confidence: 99%

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Central limit theorems for long range dependent spatial linear processes

Lahiri¹,

Robinson²

2016

Bernoulli

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Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a d-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are established for the cases of positive strong dependence, short range dependence, and negative dependence. We provide approximations to asymptotic variances that reveal differential rates of convergence under the three types of dependence. Further, in contrast to the one dimensional (i.e., the time series) case, it is shown that the form of the asymptotic variance in dimensions d > 1 critically depends on the geometry of the sampling region under positive strong dependence and under negative dependence and that there can be non-trivial edge-effects under negative dependence for d > 1. Precise conditions for the presence of edge effects are also given.

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“…We assume that the sampling region R n is obtained by "inflating" the set R 0 by the scaling factor λ n (cf. Lahiri et al [22]), that is,…”

Section: Sampling Regionsmentioning

confidence: 99%

“…In contrast to the temporal case, in most practical applications spatial sampling regions are non-rectangular, and possibly of a non-standard shape (cf. Cressie [8], Lahiri et al [22]). As a result, existing results are of limited use.…”

Section: Introductionmentioning

confidence: 99%

Central limit theorems for long range dependent spatial linear processes

Lahiri¹,

Robinson²

2016

Bernoulli

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“…For instance, various methods aim at drawing inferences for the statistical mean, by providing measures of its estimation variance and, by the way, of its uncertainty. Such methods are based either on geostatistical concepts [14][15] or on image sub-sampling, re-sampling or on block-bootstrap; see [16]- [20]. These approaches, though meant to measure the uncertainty in the estimation of statistical moments, can be used to evaluate their stationarity since the asymptotic behavior of their estimation variance closely depends on their homogeneity.…”

Section: Introductionmentioning

confidence: 99%

Assessment of Texture Stationarity Using the Asymptotic Behavior of the Empirical Mean and Variance

Blanc

Costa

Stitou

et al. 2008

IEEE Trans. on Image Process.

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“…Similar to some newer spatial analpcal techniques, such as SCDF (Overton 1989;Majure et al 1996), of which the properties and inferential power are still under investigation (Kaiser et al 1997;Lahiri et al 1999), the statistical property of LSCDF is currently not known yet. It cannot be determined at this point if it is possible to derive the statistical properties of LSCDF by analpcal methods.…”

Section: Fig 2 Circles For Selected Origin Points Determining the 0mentioning

confidence: 99%

“…Since then, Majure et al (1996) formally developed the con-cept and provided the estimation method for SCDF. More recently, the estimation and inference aspects of SCDF were further investigated (for example, Kaiser et al 1997;Lahiri et al 1999).…”

Section: -Ccmentioning

confidence: 99%

Location‐Specific Cumulative Distribution Function (LSCDF): An Alternative to Spatial Correlation Analysis

Wong¹

2001

Geographical Analysis

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Quite often, geographical analysis involves comparing the spatial distributions of two variables or attributes. A typical method isOne of the central themes in geographical analysis is to compare and evaluate the spatial distributions of different phenomena or variables in order to determine if the two phenomena or variables are related to each other. In the physical environment, one may be interested in how the spatial pattern of soil fertility level affects the amount of crop yield in different locations, or how the soil characteristics affect vegetative covers for different regions. In urban analysis, one may be interested if there is an association between income level and the level of education attainment in different parts of the city. In segregation study, the issue quite often is reduced to compare the spatial distribution patterns of different ethnic or racial groups to determine if David WS. Wong is an associate professor of geography at George Mason University.

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Prediction of Spatial Cumulative Distribution Functions Using Subsampling

Cited by 45 publications

References 0 publications

Central limit theorems for long range dependent spatial linear processes

Central limit theorems for long range dependent spatial linear processes

Assessment of Texture Stationarity Using the Asymptotic Behavior of the Empirical Mean and Variance

Location‐Specific Cumulative Distribution Function (LSCDF): An Alternative to Spatial Correlation Analysis

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