Inadmissibility of classical sharp minimax tests in high dimensional change point analysis

Beschreibung

Consider the problem of detecting changes in the mean in a high-dimensional time series.
There is, by now, a well-established theory regarding this problem, in particular from an information theoretic point of view. Motivated by a cancellation effect, we design a method that, in a certain way, renders the classical (sharp) minimax test in the sparse regime inadmissible. In extreme cases, the (sharp) minimax optimal test may have zero power with respect to certain components, whereas our method has a convincingly performance.
This phenomenon is by no means restricted to change-point problems, but may be equally observed in classical high-dimensional testing problems. Our framework is quite general and contains prominent dynamical systems such as random walks on the regular group, functionals of iterated random systems, functionals of (augmented) Garch models of any order, functionals of (Banach space valued) linear processes or possibly infinite memory Markov chains, dynamical systems arising from SDEs and many more.

Zeitraum	5 Juli 2023
Ereignistitel	European Meeting of Statisticians - EMS 2023
Veranstaltungstyp	Konferenz
Ort	Warschau, PolenAuf Karte anzeigen