On approximating the distributions of goodness-of-fit test statistics based on the empirical distribution function: the case of unknown parameters. (English) Zbl 1170.62011
Summary: This paper discusses some problems possibly arising when approximating via Monte-Carlo simulations the distributions of goodness-of-fit test statistics based on the empirical distribution function. We argue that failing to re-estimate the unknown parameters on each simulated Monte-Carlo sample – and thus avoiding to employ this information to build the test statistic – may lead to wrong, overly-conservative testing. Furthermore, we present some simple examples suggesting that the impact of this possible mistake may turn out to be dramatic and does not vanish as the sample size increases.
MSC:
| 62E17 | Approximations to statistical distributions (nonasymptotic) |
| 62G30 | Order statistics; empirical distribution functions |
| 62G10 | Nonparametric hypothesis testing |
| 65C05 | Monte Carlo methods |
Keywords:
critical values; Anderson-Darling statistic; Kolmogorov-Smirnov statistic; Kuiper statistic; Cramér-von Mises statistic; empirical distribution function; Monte-Carlo simulationsReferences:
| [1] | DOI: 10.1080/01621459.1954.10501232 · doi:10.1080/01621459.1954.10501232 |
| [2] | Babu G. J., Sankhya: The Indian Journal of Statistics 66 pp 63– |
| [3] | D’Agostino R. B., Goodness of Fit Techniques (1986) |
| [4] | DOI: 10.1214/aoms/1177728589 · Zbl 0064.13701 · doi:10.1214/aoms/1177728589 |
| [5] | DOI: 10.1093/biomet/35.1-2.182 · Zbl 0030.40503 · doi:10.1093/biomet/35.1-2.182 |
| [6] | DOI: 10.2307/2347751 · Zbl 0715.62089 · doi:10.2307/2347751 |
| [7] | DOI: 10.1007/978-1-4613-8643-8 · doi:10.1007/978-1-4613-8643-8 |
| [8] | DOI: 10.1093/biomet/62.1.5 · Zbl 0297.62027 · doi:10.1093/biomet/62.1.5 |
| [9] | DOI: 10.1093/biomet/61.1.185 · Zbl 0277.62035 · doi:10.1093/biomet/61.1.185 |
| [10] | DOI: 10.1007/978-3-642-33483-2 · doi:10.1007/978-3-642-33483-2 |
| [11] | Evans M., Statistical Distributions (2000) |
| [12] | DOI: 10.1080/01621459.1976.10481516 · doi:10.1080/01621459.1976.10481516 |
| [13] | Kuiper N. H., Proc. of the Koninklijke Nederlandse Akademie van Wetenschappen B 63 pp 38– |
| [14] | DOI: 10.1080/01621459.1967.10482916 · doi:10.1080/01621459.1967.10482916 |
| [15] | DOI: 10.1080/01621459.1951.10500769 · doi:10.1080/01621459.1951.10500769 |
| [16] | Owen D. B., A Handbook of Statistical Tables (1962) · Zbl 0102.35203 |
| [17] | Pearson E. S., Biometrika 49 pp 397– · Zbl 0011.22003 |
| [18] | DOI: 10.1080/01621459.1974.10480196 · doi:10.1080/01621459.1974.10480196 |
| [19] | DOI: 10.1214/aos/1176343411 · Zbl 0325.62014 · doi:10.1214/aos/1176343411 |
| [20] | DOI: 10.1007/BF02613687 · Zbl 0770.62016 · doi:10.1007/BF02613687 |
| [21] | DOI: 10.1201/9780203910894 · doi:10.1201/9780203910894 |
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