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arXiv · 1802.01715

A Wilks' theorem for grouped data

Emanuele Dolera·Stefano Favaro·Andrea Bulgarelli·Alessio Aboudan
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Abstract

Consider $n$ independent measurements, with the additional information of the times at which measurements are performed. This paper deals with testing statistical hypotheses when $n$ is large and only a small amount of observations concentrated in short time intervals are relevant to the study. We define a testing procedure in terms of multiple likelihood ratio (LR) statistics obtained by splitting the observations into groups, and in accordance with the following principles: P1) each LR statistic is formed by gathering the data included in $G$ consecutive vectors of observations, where $G$ is a suitable time window defined a priori with respect to an arbitrary choice of the `origin of time'; P2) the null statistical hypothesis is rejected only if at least $k$ LR statistics are sufficiently small, for a suitable choice of $k$. We show that the application of the classical Wilks' theorem may be affected by the arbitrary choice of the "origin of time", in connection with P1). We then introduce a Wilks' theorem for grouped data which leads to a testing procedure that overcomes the problem of the arbitrary choice of the `origin of time', while fulfilling P1) and P2). Such a procedure is more powerful than the corresponding procedure based on Wilks' theorem.

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Emanuele Dolera, Stefano Favaro, Andrea Bulgarelli, Alessio Aboudan. 2018-02-05. A Wilks' theorem for grouped data. https://arxiv.org/abs/1802.01715

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