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Abstract:
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We propose Narrowest Significance Pursuit (NSP), a general methodology for automatically detecting localised regions in data sequences which each must contain a change-point, at a prescribed global significance level. Here, change-points are understood as abrupt changes in the parameters of an underlying linear model. NSP works by fitting the postulated linear model over many regions of the data, using a certain multiresolution sup-norm loss, and identifying the shortest interval on which the linearity is significantly violated. The use of the multiresolution sup-norm loss is a key feature of NSP, as it guarantees important stochastic bounds which directly yield exact desired coverage probabilities, regardless of the form or number of the regressors. NSP works with a wide range of distributional assumptions on the errors, including Gaussian with known or unknown variance, some light-tailed distributions, and some heavy-tailed, possibly heterogeneous distributions via self-normalisation. In contrast to the widely studied "post-selection inference" approach, NSP enables the opposite viewpoint and paves the way for the concept of "post-inference selection".
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