Asymptotic distribution theory for contamination models

Abstract

In  many  situations  one  is  interested  in  identifying  observations  that  come  from  sources  of  variation  other  than  the  normal background  or  baseline  source.  A  simple  model  for  such  situations  is  a  two  point  mixture  model  where  one  component  in  the  mixture corresponds to the baseline model and the second to the other sources (the contamination component). Here the goal is two-fold: (i) detect the  overall  presence  of  Contamination  and  (ii)  identify  observations  that  may  be  contaminated.  A  locally  most  powerful  test  is  presented which gives  some  insights on how  to  accomplish  this. Surprisingly, the  test  statistic can have an asymptotic  distribution  that is  based  on a stable law that is not the normal distribution. Examples and simulations are given to illustrate the approach.