We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L²([0, 1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C([0, 1]). We will show that these estimators are in an adaptive sense rate optimal over certain classes of “approximation spaces.” Special cases are the class of functions of bounded variation (piecewise) Hölder continuous functions of order 0<α≤1 and the class of step functions with a finite but arbitrary number of jumps. In the latter setting, we will also deduce the rates known from change-point analysis for detecting the jumps. Finally, the issue of fully automatic selection of the smoothing parameter is addressed.

Non-cellular blood circulating microRNAs (plasma miRNAs) represent a promising source for the development of prognostic and diagnostic tools owing to their minimally invasive sampling, high stability, and simple quantification by standard techniques such as RT-qPCR. So far, the majority of association studies involving plasma miRNAs were disease-specific case-control analyses. In contrast, in the present study, plasma miRNAs were analysed in a sample of 372 individuals from a population-based cohort study, the Study of Health in Pomerania (SHIP). Quantification of miRNA levels was performed by RT-qPCR using the Exiqon Serum/Plasma Focus microRNA PCR Panel V3.M covering 179 different miRNAs. Of these, 155 were included in our analyses after quality-control. Associations between plasma miRNAs and the phenotypes age, body mass index (BMI), and sex were assessed via a two-step linear regression approach per miRNA. The first step regressed out the technical parameters and the second step determined the remaining associations between the respective plasma miRNA and the phenotypes of interest. After regressing out technical parameters and adjusting for the respective other two phenotypes, 7, 15, and 35 plasma miRNAs were significantly (q < 0.05) associated with age, BMI, and sex, respectively. Additional adjustment for the blood cell parameters identified 12 and 19 miRNAs to be significantly associated with age and BMI, respectively. Most of the BMI-associated miRNAs likely originate from liver. Sex-associated differences in miRNA levels were largely determined by differences in blood cell parameters. Thus, only 7 as compared to originally 35 sex-associated miRNAs displayed sex-specific differences after adjustment for blood cell parameters. These findings emphasize that circulating miRNAs are strongly impacted by age, BMI, and sex. Hence, these parameters should be considered as covariates in association studies based on plasma miRNA levels. The established experimental and computational workflow can now be used in future screening studies to determine associations of plasma miRNAs with defined disease phenotypes.

We discuss the interplay between local M -smoothers, Bayes smoothers and some nonlinear filters for edge-preserving signal reconstruction. We prove that all smoothers in question are nonlinear filters in a precise sense and characterize their fixed points. Then a Potts model is adopted for segmentation. For 1-d signals, an exact algorithm for the computation of maximum posterior modes is derived and applied to a phantom and to 1-d fMRI-data.