Empirical-distribution-function goodness-of-fit tests for discrete models. (English) Zbl 0846.62037
Summary: We present a simple framework for studying empirical-distribution-function goodness-of-fit tests for discrete models. A key tool is a weak-convergence result for an estimated discrete empirical process, regarded as a random element in some suitable sequence space. Special emphasis is given to the problem of testing for a Poisson model and for the geometric distribution. Simulations show that parametric bootstrap versions of the tests maintain a nominal level of significance very closely even for small samples where reliance upon asymptotic critical values is doubtful.
MSC:
| 62G10 | Nonparametric hypothesis testing |
| 62G30 | Order statistics; empirical distribution functions |
| 62F03 | Parametric hypothesis testing |
Keywords:
simulations; empirical-distribution-function; goodness-of-fit tests; discrete models; weak-convergence result; estimated discrete empirical process; Poisson model; geometric distribution; parametric bootstrap; level of significance; critical valuesReferences:
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