Localising change points in piecewise polynomials of general degrees

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 results by deriving global information-theoretic lower bounds, which show that our estimators nearly minimax rate-optimal. also estimator enjoys near optimally adaptive performance attaining individual errors level smoothness at change points signal. addition, under special constraint, bound errors. This is orders sharper than bound.