Estimating and testing circular orders for cell cycle genes expression data

Abstract

Analysis of angular data has a long history with well-developed theory and methodology documented in several books [cf. Fisher (1993), Mardia and Jupp (2000)]. Most of the theory have been developed several decades ago. However, in recent years, and motivated by the applications, there has been a reawaked interest in drawing inferences regarding angular parameters. In particular, in the biology field to analyze periodic patterns of gene expressions. These patterns show the contribution of the genes in oscillatory biological processes, such as the cell-cycle, the circadian clock or the metabolic cycle. The time to peak expression (known as the phase angle) of such a gene can be mapped onto a unit circle and is an angular parameter.