Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement

Zhenguo Gao

Abstract:

Literature on change point analysis mostly requires a sudden change in the data distribution, either in
a few parameters or the distribution as a whole. We are interested in the scenario, where the variance of
data may make a significant jump while the mean changes in a smooth fashion. The motivation is a liver
procurement experiment monitoring organ surface temperature. Blindly applying the existing methods to
the example can yield erroneous change point estimates since the smoothly changing mean violates the
sudden-change assumption. We propose a penalized weighted least-squares approach with an iterative
estimation procedure that integrates variance change point detection and smooth mean function estimation. The procedure starts with a consistent initial mean estimate ignoring the variance heterogeneity.
Given the variance components the mean function is estimated by smoothing splines as the minimizer of
the penalized weighted least squares. Given the mean function, we propose a likelihood ratio test statistic
for identifying the variance change point. The null distribution of the test statistic is derived together with
the rates of convergence of all the parameter estimates. Simulations show excellent performance of the
proposed method. Application analysis offers numerical support to non invasive organ viability assessment
by surface temperature monitoring. Supplementary materials for this article are available online.