Inference for the Broken-Stick Model: A Computationally Faster Approach

• Activity Number: 46
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Ritabrata Das*+ and Moulinath Banerjee and Bin Nan
• Companies: and University of Michigan and University of Michigan
• Keywords: broken-stick model ; change-point ; Newton-Raphson ; asymptotics ; computational economy ; smoothing

Abstract

The existence of one or more change-points in linear regression problems has significant applications in climate data, economic time series and for modeling biological processes, where the change-points mostly pertain to the onset of biologically important phenomena. Estimation of change-point(s) in a broken-stick model using the exact likelihood has been discussed in some depth in the literature but most of the methods are computationally quite expensive: the non-differentiability at the kink(s) necessitates an exhaustive search across tuples of order statistics. In this article, we present a smoothing based approach to address this difficulty. We smooth the broken-stick in a shrinking neighborhood of the kinks by quadratic functions and use this as our working model, which allows the use of Newton-Raphson type methods for the working likelihood function. Asymptotic properties of our estimates are presented. We find that our estimates converge at square-root rate and are fully efficient. Simulations clearly vindicate the computational economy of our approach with quite remarkable gains in computation times for the two change points problem.