Jump information criterion for statistical inference in estimating discontinuous curves

Nonparametric regression analysis when the regression function is discontinuous has many applications. Existing methods for estimating a discontinuous regression curve usually assume that the number of jumps in the regression curve is known beforehand, which is unrealistic in some situations. Although there has been research on estimation of a discontinuous regression curve when the number of jumps is unknown, the problem remains mostly open because such research often requires assumptions on other related quantities, such as a known minimum jump size. In this paper we propose a jump information criterion which consists of a term measuring the fidelity of the estimated regression curve to the observed data and a penalty related to the number of jumps and the jump sizes. The number of jumps can then be determined by minimizing our criterion. Theoretical and numerical studies show that our method works well.

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