A Wilks' theorem for grouped data [article]

Emanuele Dolera, Stefano Favaro, Andrea Bulgarelli, Alessio Aboudan
2018 arXiv   pre-print
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
more » ... s 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.
arXiv:1802.01715v3 fatcat:5ejf74dhlrenzbsffa4r3ln7hi