Are deviations in a gradually varying mean relevant? A testing approach based on sup-norm estimators

Discovering a change point in a time series of organoid networks via the iso-mirror

“…In addition, it remains to study the entry-wise behavior of the error term (t) = ψ(t) − ψ(t). For example: in [3] the proof of consistency of the change point estimator requires the error process to be stationary; in [4] the (t) are assumed to be i.i.d. normal to construct a confidence interval for t * .…”

“…Both the change point detection algorithm from [3] and the break point estimation for piecewise linear models from [4] yield an estimated change point t * = 4, day 188, which coincides with neuroscientifically significant developmental changesinhibitory neurons start appearing and the percentage of astrocytes increases dramatically -as described in [10]. Note that the emergence of astrocytes does not happen at once but builds over time, so there is no one precise date for the change point and detection of a time coinciding with this change can be but suggestive.…”

“…Thence, mirror estimation and manifold learning recovers a 1-dimensional piecewise linear 'iso-mirror' representation, with an evident slope change. By using the change point detection algorithm from [3] and break point estimation for piecewise linear models from [4],…”

Sharp adaptive similarity testing with pathwise stability for ergodic diffusions

“…But even if the reference b 0 is available, testing b = b 0 may miss the point in many applications because 'sufficiently close' is equally convenient. The relevance of testing hypotheses of the form (1.1) for η > 0 has meanwhile been widely acknowledged in many different fields of statistical inference such as financial, medical, pharmaceutical or environmental statistics, see [3], [9], [14], [23], [43], [50] and [58] including references cited therein. Note that testing for similarity avoids the consistency problem mentioned in [6], i.e.…”