Abstract
Some goodness-of-fit tests based on the L 1-norm are considered. The asymptotic distribution of each statistic under the null hypothesis is the distribution of the L 1-norm of the standard Wiener process on [0,1]. The distribution function, the density function and a table of some percentage points of the distribution are given. A result for the asymptotic tail probability of the L 1-norm of a Gaussian process is also obtained. The result is useful for giving the approximate Bahadur efficiency of the test statistics whose asymptotic distributions are represented as the L 1-norms of Gaussian processes.
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Aki, S., Kashiwagi, N. Asymptotic properties of some goodness-of-fit tests based on the L 1-norm. Ann Inst Stat Math 41, 753–764 (1989). https://doi.org/10.1007/BF00057739
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DOI: https://doi.org/10.1007/BF00057739