Autocovariance estimation in regression with a discontinuous signal and mm-dependent errors: A difference-based approach

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 $\sqrt{n}$-consistency; this result is extended to piecewise Holder 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.Comment: 41 pages, 3 figures, 3 table

Fully-Automatic Multiresolution Idealization for Filtered Ion Channel Recordings: Flickering Event Detection

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 methodolodgy 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

Indice extremo en procesos heteroscedásticos

Una aplicación de la teoría de valores extremos al análisis de series de tiempo, esta es una buena manera de resumir nuestro trabajo

TATSSI: A Free and Open-Source Platform for Analyzing Earth Observation Products with Quality Data Assessment

Earth observation (EO) data play a crucial role in monitoring ecosystems and environmental processes. Time series of satellite data are essential for long-term studies in this context. Working with large volumes of satellite data, however, can still be a challenge, as the computational environment with respect to storage, processing and data handling can be demanding, which sometimes can be perceived as a barrier when using EO data for scientific purposes. In particular, open-source developments which comprise all components of EO data handling and analysis are still scarce. To overcome this difficulty, we present Tools for Analyzing Time Series of Satellite Imagery (TATSSI), an open-source platform written in Python that provides routines for downloading, generating, gap-filling, smoothing, analyzing and exporting EO time series. Since TATSSI integrates quality assessment and quality control flags when generating time series, data quality analysis is the backbone of any analysis made with the platform. We discuss TATSSI’s 3-layered architecture (data handling, engine and three application programming interfaces (API)); by allowing three APIs (a native graphical user interface, some Jupyter Notebooks and the Python command line) this development is exceptionally user-friendly. Furthermore, to demonstrate the application potential of TATSSI, we evaluated MODIS time series data for three case studies (irrigation area changes, evaluation of moisture dynamics in a wetland ecosystem and vegetation monitoring in a burned area) in different geographical regions of Mexico. Our analyses were based on methods such as the spatio-temporal distribution of maxima over time, statistical trend analysis and change-point decomposition, all of which were implemented in TATSSI. Our results are consistent with other scientific studies and results in these areas and with related in-situ data