On the Prequential Approach for Testing Exponentiality

Mhamed-Ali El Aroui 1
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive
Abstract : We present a prequential (predictive-sequential) approach for testing the goodness-of-fit of an exponential distribution when the parameter $\lambda$ is unknown. Instead of using all the available observations, $\lambda$ is estimated by a prequential approach where at each step $i$, only the $i\!-\!1$ first observations are used. We show that this approach provides a sequence of \ks type distances whose expressions do not depend on $\lambda$ and which converge in distribution (under the null hypothesis) to the \ks distribution. This leads to a simple technique for testing the goodness-of-fit of exponential distributions with unknown parameter using standard quantile tables of the \ks distribution. Even if Monte~Carlo simulations show that the prequential test is less powerful than the standard exponentiality test, the developed results represent a first step in the theoretical study of the {\it u-plot} which is a prequential empirical tool commonly used for the validation of reliability-growth models.
Type de document :
Rapport
RR-3082, INRIA. 1997
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Soumis le : mercredi 24 mai 2006 - 13:18:29
Dernière modification le : jeudi 28 juin 2018 - 14:36:52
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Mhamed-Ali El Aroui. On the Prequential Approach for Testing Exponentiality. RR-3082, INRIA. 1997. 〈inria-00073609〉

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