  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.
