Asymptotic properties of some goodness-of-fit tests based on the L1-norm
- Resource Type
- Article
- Authors
- Aki, Sigeo; Kashiwagi, Nobuhisa
- Source
- Annals of the Institute of Statistical Mathematics; December 1989, Vol. 41 Issue: 4 p753-764, 12p
- Subject
- Language
- ISSN
- 00203157; 15729052
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.