Bootstrapping the Empirical Distribution Function of a Spatial Process

Zhu, Jun; Lahiri, Soumendra N.

doi:10.1007/s11203-005-2349-4

Cited by 10 publications

(7 citation statements)

References 32 publications

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“…Block bootstrap and subsampling for random fields were proposed by Hall (1985) and Künsch (1989), whereas Politis and Romano (1993) addressed block resampling schemes for general statistics. Zhu and Lahiri (2007) proved bootstrap consistency for the empirical process of a non-overlapping block bootstrap. Optimal block size and subsample size selection have been addressed in Nordman and Lahiri (2007) and Nordman and Lahiri (2004), respectively.…”

Section: Introductionmentioning

confidence: 95%

Baxter’s inequality and sieve bootstrap for random fields

Meyer¹,

Jentsch²,

Kreiß³

2017

Bernoulli

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Abstract. The concept of the autoregressive (AR) sieve bootstrap is investigated for the case of spatial processes in Z 2 . This procedure fits AR models of increasing order to the given data and, via resampling of the residuals, generates bootstrap replicates of the sample. The paper explores the range of validity of this resampling procedure and provides a general check criterion which allows to decide whether the AR sieve bootstrap asymptotically works for a specific statistic of interest or not. The criterion may be applied to a large class of stationary spatial processes. As another major contribution of this paper, a weighted Baxter-inequality for spatial processes is provided. This result yields a rate of convergence for the finite predictor coefficients, i.e. the coefficients of finite-order AR model fits, towards the autoregressive coefficients which are inherent to the underlying process under mild conditions.The developed check criterion is applied to some particularly interesting statistics like sample autocorrelations and standardized sample variograms. A simulation study shows that the procedure performs very well compared to normal approximations as well as block bootstrap methods in finite samples.

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Section: Introductionmentioning

confidence: 95%

Baxter’s inequality and sieve bootstrap for random fields

Meyer¹,

Jentsch²,

Kreiß³

2017

Bernoulli

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“…In addition, an α-mixing condition will be established for the random process, similar to that imposed in Zhu and Lahiri [20]. For this purpose, given…”

Section: Main Hypothesismentioning

confidence: 99%

Convergence in distribution of the L2-deviations of the kernel-type variogram estimators with applications

García-Soidán

Cotos-Yáñez

2017

Spatial Statistics

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In this work, some properties of the L 2-deviations of the Nadaraya-Watson variogram estimators are analyzed, for both the anisotropic and the isotropic settings. Their convergence in distribution is established, which provides the basis for addressing practical problems, such as the construction of goodness of fit tests for the variogram and, therefore, for modeling the spatial dependence. However, the development of the latter application requires solving different issues, such as the approximation of the model parameters and the critical points. For estimation of the former ones, we propose proceeding through the least squares criteria, whose consistency will be proved, together with a reformulation of the global measures for the kernel-type estimators. Then, the resulting critical points can be approximated by appealing to the bootstrap approaches. Numerical studies with simulated and real data have been developed to illustrate the potentiality of our results, in order to check the appropriateness of a variogram model selected for the variogram.

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“…In both examples, a spatial block bootstrap resampling method is applied. This block bootstrap procedure is proved to be consistent in Zhu and Lahiri (2007 In our case, we are interested in detecting changes on the dependence structure and, for that purpose, we will consider a spectral approach.…”

Section: A New Test For Comparing Spatial Log-spectral Densitiesmentioning

confidence: 99%

Comparing spatial dependence structures using spectral density estimators

2007

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SUMMARYThe aim of this work is to establish statistical methodology in order to analyze changes in the dependence structure for different spatial processes or for a process observed on a regular grid at different time moments. We propose a test statistic for testing the hypothesis H 0 : f 1 = f 2 , where each f l denotes the spectral density of each process, for l = 1, 2. The test is based on a Cramer-von-Mises functional type test introduced in (Vilar-Fernández and González-Manteiga, 2004) for the regression context. The study is developed for L = 2, but generalizations to L > 2 are straightforward. The application of our technique is related to biomonitoring studies which have been carried out in order to determine levels of heavy metal concentrations, taking mosses as biomonitors.

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Bootstrapping the Empirical Distribution Function of a Spatial Process

Abstract: functional central limit theorem, increasing domain asymptotics, infill asymptotics, resampling, α-mixing random field,

Cited by 10 publications

References 32 publications

Baxter’s inequality and sieve bootstrap for random fields

Baxter’s inequality and sieve bootstrap for random fields

Convergence in distribution of the L2-deviations of the kernel-type variogram estimators with applications

Comparing spatial dependence structures using spectral density estimators

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