Asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling method

• 成果类型: Article
• 署名作者: Lahiri, SN
• 署名单位: Iowa State University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400050221
• 发表日期: 1999
• 页码: 55-84
• 关键词: central limit-theorem; random-fields

摘要

A spatial cumulative distribution function (F) over cap(infinity) (say) is a random distribution function that provides a statistical summary of random field over a given region. This paper considers the empirical predictor of (F) over cap(infinity) based on a finite set of observations from a region in R-d under a uniform sampling design. A functional central limit theorem is proved for the predictor as a random element of the space D[-infinity, infinity]. A striking feature of the result is that the rate of convergence of the predictor to the predict and (F) over cap(infinity) depends on the location of the data-sites specified by the sampling design. A precise description of the dependence is given. Furthermore, a subsampling method is proposed for integral-based functionals of random fields, which is then used to construct large sample prediction bands for (F) over cap(infinity).