Conference Agenda

A novel self-normalization procedure for CUSUM-based change detection in the mean of a locally stationary time series is introduced. Classical self-normalization relies on the factorization of a constant long-run variance and a stochastic factor. In this case, the CUSUM statistic can be divided by another statistic proportional to the long-run variance, so that the latter cancels. Thereby, a tedious estimation of the long-run variance can be avoided. Under local stationarity, the partial sum process converges to $int_0^t sigma(x) dBx$ and no such factorization is possible. To overcome this obstacle, a self-normalized test statistic is constructed from a carefully designed bivariate partial-sum process. Weak convergence of the process implies that the resulting self-normalized test attains asymptotic level α under the null hypothesis of no change, while being consistent against a broad class of alternatives. Extensive simulations demonstrate better finite-sample properties compared to existing methods. Applications to real data illustrate the method’s practical effectiveness.

We study estimation of a class prior for unlabeled target samples which possibly differs from that of source population. Moreover, it is assumed that the source data is partially observable: only samples from the positive class and from the whole population are available (PU learning scenario). We introduce a novel direct estimator of the class prior which avoids estimation of posterior probabilities in both populations and has a simple geometric interpretation. It is based on a distribution matching technique together with kernel embedding in Reproducing Kernel Hilbert Space and is obtained as an explicit solution to an optimisation task. We establish its asymptotic consistency as well as an explicit non-asymptotic bound on its deviation from the unknown prior, which is calculable in practice. We study finite sample behaviour for synthetic and real data and show that the proposal works consistently on par or better than its competitors.

Control statistics are widely used to monitor the quality of processes in various fields such as industry, healthcare, and machine learning. These statistics give an alarm when observed data exceed a threshold, traditionally set as a constant value to maintain a desired false alarm rate. Now we want to focus on a new setting: When monitoring a sequence of observations, there may be additional information that potentially affects the law of the observations, and we would like to change the design by using adapted thresholds, which are functions of the additional information.
So far, we have considered several classes of adaptive threshold functions for continuous observations, including constant, proportional, and dominated classes. Our focus is on the proportional class threshold, which adjusts the sensitivity automatically based on the external information, making it particularly effective in detecting rare but critical cases. We derive an estimator for this threshold function using kernel density estimation and establish its consistency, asymptotic normality and some further asymptotic properties. Additionally, we demonstrate the application of this method for real car engine data, where we monitor the engine revolutions per minute (RPM) using lubrication pressure as external information to assess the performance of this method.