Semiparametric single index multi change points model with an application of environmental health study on mortality and temperature

Abstract

Many studies have considered the effect of temperature and a change point in association with increased mortality. However, the relationship between temperature and mortality cannot be described using a parametric model and is highly dependent on the number of change points. Knowing the change points of temperature may prevent further mortality associated with the weather. The current available methods consist of two steps: they first estimate the models and then detect change points without testing. However, the methods for simultaneously identifying the nonlinear relationship and detecting the number of change points are quite limited. Therefore, in this paper, we propose a unified approach simultaneously estimates the nonlinear relationship and detects multichange points. We propose a semiparametric single index multichange points model as our unified approach by adjusting for several other covariates. We also provide a permutation-based testing procedure to detect multichange points. A criterion for predetermining the maximum possible number of change points is introduced, which is required by the permutation test procedure. Our approach is unaffected by the degree of smoothing of the nonparametric function. Our proposed model is compared to the generalized linear model and generalized additive model using simulation and a real application. Our approach outperforms these models in both model fitting and detection of change point(s). We also show the asymptotic properties of the permutation test for semiparametric single index multichange points model, suggesting that the number of change points is consistent. The advantage of our approach is demonstrated using the mortality data of Seoul, South Korea.