Abstract:

Biomarker combinations are becoming a common tool for the early detection of serious medical conditions such as sepsis. Indirect methods of measuring biomarker concentrations are preferred due to their speed and reliability; however, these methods can only measure concentrations within a limited regime, leading to a missing data problem. Because the missingness in this problem is not ignorable, we develop a novel imputation method based on matrix factorization that explicitly models the partial interval censoring. We further develop an empirical Bayes formulation of the problem that improves the estimation properties.

Abstract:

The detection and estimation of change point(s) have applications in many areas, whereas most methods in the literature are applicable only under a specific dimensional setting. Motived by this limitation, we propose a dimension-agnostic procedure of single change-point testing for time series by incorporating the idea of sample splitting and self-normalization. We propose test statistics against both dense and sparse changes in mean and derive the limit when the sample size diverges, regardless of the dimensionality. The asymptotic power against the local alternative is also investigated. The encouraging numerical results demonstrate the effectiveness of our method in detecting and estimating the change point(s) for a broad range of dimensions.