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High precision implementation of Steck's recursion method for use in goodness-of-fit tests
Jiefei Wang1, Jeffrey C Miecznikowski1
1Department of Biostatistics, SUNY University at Buffalo, Buffalo, NY, USA.
Abstract:
Classical continuous goodness-of-fit (GOF) testing is employed for examining whether the data come from an assumed parametric model. In many cases, GOF tests assume a uniform null distribution and examine extreme values of the order statistics of the samples. Many of these statistics can be expressed by a function of the order statistics and the p-values amount to a joint probability statement based on the uniform order statistics. In this paper, we utilize Steck's recursion method and propose two high precision computing algorithms to compute the p-values for these GOF statistics. The numerical difficulties in implementing Steck's method are discussed and compared with solutions provided in high precision libraries.
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