Asymptotic properties of some goodness-of-fit tests based on the L 1-norm |
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| Authors: | Sigeo Aki Nobuhisa Kashiwagi |
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| Affiliation: | (1) The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106 Tokyo, Japan;(2) Present address: Faculty of Law and Economics, Chiba University, Yayoi-cho, 260 Chiba, Japan |
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| Abstract: | Some goodness-of-fit tests based on the L1-norm are considered. The asymptotic distribution of each statistic under the null hypothesis is the distribution of the L1-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 L1-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 L1-norms of Gaussian processes. |
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| Keywords: | Asymptotic distribution approximate Bahadur efficiency L1-norm empirical process goodness-of-fit tests martingale symmetry Wiener process |
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