A Minimax Contrast for the Isotonic Change-Point Problem

• Activity Number: 168
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Karl D'Silva*+
• Companies: North Dakota State University
• Keywords: change-point ; isotonic ; minimax ; contrast ; dependence ; U-statistic

Abstract

A change in model parameters over time often characterizes major events. Situations in which this may arise include increasing temperatures, intense rainfall, and the valuation of a stock. The question is whether these observations are simply the result of natural variation, or rather are indicative of an underlying monotonic trend. This is known as the isotonic change-point problem. We shall justify and utilize the minimax criterion in order to identify the optimal test statistic within a specified class. It will be seen that, as motivated by the projection method, the aforementioned class is the class of contrasts. It shall be proven that the set of coefficients originally proposed by Abelson and Tukey (1963), and utilized by Brillinger (1989) in the isotonic change-point setting, are in fact minimax in the independent data case. For correlated data with short-range dependence, we shall demonstrate a sufficient condition for minimaxity to hold.