Some advances in constrained inference for ordered circular parameters in oscillatory systems

Abstract

Constraints on parameters arise naturally in many applications. Statistical methods that honor the underlying constraints tend to be more powerful and result in better interpretation of the underlying scientific data. In the context of Euclidean space data, there exists over five decades of statistical literature on constrained statistical inference and at least four books on the subject (e.g. Robertson et al. 1988; Silvapulle and Sen 2005). However, it was not until recently that these methods have been used extensively in applied research. For example, constrained statistical inference is gaining considerable interest among applied researchers in a variety of fields, such as, for example, toxicology (Peddada et al. 2007), genomics (Hoenerhoff et al. 2013; Perdivara et al. 2011; Peddada et al. 2003), epidemiology (Cao et al. 2011; Peddada et al. 2005), clinical trials (Conaway et al. 2004), or cancer trials (Conde et al. 2012, 2013).