We study the detection of a sparse change in high-dimensional mean vector as minimax testing problem. Our first main contribution is to derive exact rate across all parameter regimes for n independent, p-variate Gaussian observations. This exhibits phase transition when sparsity level order ploglog(8n) and has very delicate dependence on sample size: certain regime, it involves triple iterated ...

Abstract: The aim of the present investigation is to study the physical and mechanical characteristics of dental-filling spherical high-copper and silver amalgams and to compare them with a common high-copper domestic unicompositional amalgam. In this study, cylindrical specimens were mechanically condensed according to the ISO 1559:1986 Standard in order to measure the compressive strength, Vi...

In this article, we propose a class of test statistics for change point in the mean high-dimensional independent data. Our integrates U-statistic based approach recent work by Wang et al. and Lq-norm He al., inherits several appealing features such as being tuning parameter free asymptotic independence corresponding to even q’s. A simple combination different q’s leads with adaptive power prope...