On approximate validation of models: A Kolmogorov-Smirnov based approach
| Autor: | E. del Barrio, Carlos Matrán, Hristo Inouzhe |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
False discovery rate FOS: Computer and information sciences Estimator Mathematics - Statistics Theory Statistics Theory (math.ST) Kolmogorov–Smirnov test Infimum and supremum Methodology (stat.ME) symbols.namesake Metric (mathematics) symbols FOS: Mathematics Applied mathematics Statistics Probability and Uncertainty Gaussian process Statistic Statistics - Methodology Mathematics Type I and type II errors |
| DOI: | 10.48550/arxiv.1903.08687 |
| Popis: | Classical tests of fit typically reject a model for large enough real data samples. In contrast, often in statistical practice a model offers a good description of the data even though it is not the "true" random generator. We consider a more flexible approach based on contamination neighbourhoods around a model. Using trimming methods and the Kolmogorov metric we introduce a functional statistic measuring departures from a contaminated model and the associated estimator corresponding to its sample version. We show how this estimator allows testing of fit for the (slightly) contaminated model vs sensible deviations from it, with uniformly exponentially small type I and type II error probabilities. We also address the asymptotic behavior of the estimator showing that, under suitable regularity conditions, it asymptotically behaves as the supremum of a Gaussian process. As an application we explore methods of comparison between descriptive models based on the paradigm of model falseness. We also include some connections of our approach with the False-Discovery-Rate setting, showing competitive behavior when estimating the contamination level, although applicable in a wider framework. Comment: 14 figures, 32 pages |
| Databáze: | OpenAIRE |
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