A. Bücher, H. Dette, F. Heinrichs
Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly nonstationary time series and at (2) identifying regions where the mean exhibits a piecewise constant behavior. In many applications however, it is more reasonable to assume that the mean changes gradually in a smooth way. Those gradual changes may either be nonrelevant (i.e., small), or relevant for a specific problem at hand, and in this talk we aim to detect the latter. More precisely, we consider the common nonparametric regression model X_i=μ(i/n)+ε_i with centered errors and propose a test for the null hypothesis that the maximum absolute deviation of the regression function μ from a functional g(μ) (such as the value μ(0) or the integral ∫μ(t)dt) is smaller than a given threshold on a given interval [x0,x1]⊆[0,1]. A test for this type of hypotheses is developed and its asymptotic properties are investigated.
Keywords: Gaussian approximation, gradual changes, Gumbel distribution, local-linear estimator, maximum deviation, relevant change point analysis
Scheduled
Nonparametric Statistics
June 10, 2022 4:00 PM
A13
