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Abstract:
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Multiple change point detection has become popular with the routine collection of complex non stationary time series. An equally important but comparatively neglected question concerns quantifying the level of uncertainty around each putative change point. Though a handful of procedures exist in the literature, most all make assumptions on the density of the contaminating noise which are impossible to verify in practice. Moreover, most procedures are only applicable in the canonical piecewise-constant mean (median, or quantile) setting. We present a procedure which, under minimal assumptions, returns localised regions of a data sequence which must contain a change point at some global significance level chosen by the user. Our procedure is based on properties of confidence sets for the underlying regression function obtained by inverting certain multi-resolution tests, and is immediately applicable to change points in higher order polynomials. We will discuss some appealing theoretical properties of our procedure, and show its good practical performance on real and simulated data.
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