Sankhya: The Indian Journal of Statistics

2007, Volume 69, Pt. 3, 468--493

Optimal Block Size for Variance Estimation by a Spatial Block Bootstrap Method

Daniel J. Nordman and Soumendra N. Lahiri, Iowa State University, Ames, USA
Brooke L. Fridley, Mayo Clinic, Rochester, USA

SUMMARY. This paper considers the block selection problem for a block bootstrap variance estimator applied to spatial data on a regular grid. We develop precise formulae for the optimal block sizes that minimize the mean squared error of the bootstrap variance estimator. We then describe practical methods for estimating these spatial block sizes and prove the consistency of a block selection method by Hall, Horowitz and Jing (1995), originally introduced for time series. The spatial block bootstrap method is illustrated through data examples, and its performance is investigated through several simulation studies.

AMS (2000) subject classification. Primary 62G09; secondary 62M30.

Key words and phrases. Block bootstrap, empirical block choice, stationary random fields.

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