A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics

Efron (1979) introduced the bootstrap method for independent data but it cannot be easily applied to spatial data because of their dependency. For spatial data that are correlated in terms of their locations in the underlying space the moving block bootstrap method is usually used to estimate the precision measures of the estimators. The precision of the moving block bootstrap estimators is related to the block size which is difficult to select. In the moving block bootstrap method also the variance estimator is underestimated. In this paper, first the semi-parametric bootstrap is used to estimate the precision measures of estimators in spatial data analysis. In the semi-parametric bootstrap method, we use the estimation of the spatial correlation structure. Then, we compare the semi-parametric bootstrap with a moving block bootstrap for variance estimation of estimators in a simulation study. Finally, we use the semi-parametric bootstrap to analyze the coal-ash data.

[1]  Ronald Christensen.  Prediction of Spatial Cumulative Distribution Functions Using Subsampling: Comment , 1999 .

[2]  A. Bose.  Edgeworth correction by bootstrap in autoregressions , 1988 .

[3]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[4]  N. Cressie,et al.  Mean squared prediction error in the spatial linear model with estimated covariance parameters , 1992 .

[5]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[6]  Efstathios Paparoditis,et al.  Resampling Marked Point Processes , 1999 .

[7]  Peter Hall.  Resampling a coverage pattern , 1985 .

[8]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[9]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[10]  Edward Carlstein,et al.  Nonparametric Estimation of the Moments of a General Statistic Computed from Spatial Data , 1994 .

[11]  Kanti V. Mardia,et al.  Spectral and circulant approximations to the likelihood for stationary Gaussian random fields , 1996 .

[12]  Joseph P. Romano,et al.  Nonparametric Resampling for Homogeneous Strong Mixing Random Fields , 1993 .

[13]  S. Lahiri.  Resampling Methods for Dependent Data , 2003 .

[14]  K. Singh,et al.  On the Asymptotic Accuracy of Efron's Bootstrap , 1981 .

[15]  Efstathios Paparoditis,et al.  LARGE SAMPLE INFERENCE FOR IRREGULARLY SPACED DEPENDENT OBSERVATIONS BASEDON SUBSAMPLING , 1998 .

[16]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[17]  Hans R. Künsch,et al.  Prediction of Spatial Cumulative Distribution Functions Using Subsampling: Comment , 1999 .

[18]  Noel A Cressie,et al.  Prediction of spatial cumulative distribution functions using subsampling , 1999 .

[19]  K. Mardia,et al.  Maximum likelihood estimation of models for residual covariance in spatial regression , 1984 .

[20]  M. Mohammadzadeh,et al.  Spectral Approximation to the Likelihood for an Intrinsic Gaussian Random Field , 1999 .

[21]  Daniel J. Nordman,et al.  On optimal spatial subsample size for variance estimation , 2002 .

[22]  Soumendra N. Lahiri,et al.  A nonparametric plug-in rule for selecting optimal block lengths for block bootstrap methods ☆ , 2007 .

[23]  Antonio Possolo,et al.  Subsampling a random field , 1991 .

[24]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[25]  Regina Y. Liu.  Moving blocks jackknife and bootstrap capture weak dependence , 1992 .

[26]  Joseph P. Romano,et al.  Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions , 1994 .

[27]  D. Freedman,et al.  Bootstrapping a Regression Equation: Some Empirical Results , 1984 .

[28]  M. Sherman.  Variance Estimation for Statistics Computed from Spatial Lattice Data , 1996 .

[29]  Kanti V. Mardia,et al.  On bias in maximum likelihood estimators , 1999 .