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A Wilks' theorem for grouped data
- Publication Year :
- 2018
-
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.<br />Comment: arXiv admin note: text overlap with arXiv:1411.0947
- Subjects :
- Statistics - Methodology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1802.01715
- Document Type :
- Working Paper