This paper proposes a new test for change point in the mean of high-dimensional data based on spatial sign and self-normalization. The is easy to implement with no tuning parameters, robust heavy-tailedness theoretically justified both fixed-n sequential asymptotics under null alternatives, where n sample size. We demonstrate that provide better approximation finite distribution thus should be ...

A general class of recursive residuals is incorporated in the formulation of suitable (aligned) rank tests for change-points pertaining to some simple linear models. The asymptotic theory of the proposed tests rests on some invariance principles for recursively aligned signed rand statistics, and these are developed. Along with the asymptotic properties of the proposed tests, allied efficiency ...

Tests for change-points for location or regression models are often based on cumulative sums of recursive residuals. In the context of general estimable parameters (functionals of the underlying distributions), such recursive residuals may be defined in terms of recursive U-statistics. Along with some invariance principles for recursive U-statistics, asymptotic properties of some proposed tests...

In this paper we are concerned with a sequence of univariate random variables piecewise polynomial means and independent sub-Gaussian noise. The underlying polynomials allowed to be arbitrary but fixed degrees. All the other model parameters vary depending on sample size. We propose two-step estimation procedure based ℓ0-penalisation provide upper bounds localisation error. complement these res...