Nonparametric product partition models for multiple change-points analysis

Abstract

ABSTRACTWe propose an extension of parametric product partition models. We name our proposal nonparametric product partition models because we associate a random measure instead of a parametric kernel to each set within a random partition. Our methodology does not impose any specific form on the marginal distribution of the observations, allowing us to detect shifts of behaviour even when dealing with heavy-tailed or skewed distributions. We propose a suitable loss function and find the partition of the data having minimum expected loss. We then apply our nonparametric procedure to multiple change-point analysis and compare it with PPMs and with other methodologies that have recently appeared in the literature. Also, in the context of missing data, we exploit the product partition structure in order to estimate the distribution function of each missing value, allowing us to detect change points using the loss function mentioned above. Finally, we present applications to financial as well as genetic data.