We propose a new model-free segmentation method, JULES, which combines recent statistical multiresolution techniques with local deconvolution for idealization of ion channel recordings. The multiresolution criterion takes into account scales down to the sampling rate enabling the detection of flickering events, i.e., events on small temporal scales, even below the filter frequency. For such small scales the deconvolution step allows for a precise determination of dwell times and, in particular, of amplitude levels, a task which is not possible with common thresholding methods. This is confirmed theoretically and in a comprehensive simulation study. In addition, JULES can be applied as a preprocessing method for a refined hidden Markov analysis. Our new methodology allows us to show that gramicidin A flickering events have the same amplitude as the slow gating events. JULES is available as an R function jules in the package clampSeg.

Abstract. We discuss a class of difference-based estimators for the autocovariance in nonparametric regression when the signal is discontinuous (change-point regression), possibly highly fluctuating, and the errors form a stationary m-dependent process. These estimators circumvent the explicit pre-estimation of the unknown regression function, a task which is particularly challenging for such signals. We provide explicit expressions for their mean squared errors when the signal function is piecewise constant (segment regression) and the errors are Gaussian. Based on this we derive biased-optimized estimates which do not depend on the particular (unknown) autocovariance structure. Notably, for positively correlated errors, that part of the variance of our estimators which depends on the signal is minimal as well. Further, we provide sufficient conditions for √ n-consistency; this result is extended to piecewise Hölder regression with non-Gaussian errors.We combine our biased-optimized autocovariance estimates with a projection-based approach and derive covariance matrix estimates, a method which is of independent interest. Several simulation studies as well as an application to biophysical measurements complement this paper.

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We discuss a class of difference-based estimators of the autocovariance function in a semiparametric regression model where the signal consists of the sum of an identifiable smooth function and another function with jumps (change points) and the errors are m-dependent. We establish that the influence of the smooth part of the signal over the bias of our estimators is negligible; this result does not depend on any distributional assumption. Under Gaussianity of the errors, we show that the mean squared error of the proposed estimators does not depend on either the unknown smooth function or on the values of the difference sequence coefficients; our finite sample studies suggest that the latter feature holds true regardless of the Gaussianity assumption. We also allow that both the number of change points and the magnitude of the largest jump grow with the sample size. In this case, we provide conditions on the interplay between the growth rate of these two quantities in order to ensure √ n consistency of our estimators.