Model specification testing is one of the essential methodological tasks in statistics. Recently, with the development of different data structures, envisioning concepts from classical data setups to other environments becomes very important. In the webinar, selected young statisticians will present their recent works end elaborate on different aspects of this topic. Speakers: – Thomas Berrett, University of Warwick, United Kingdom: Hypothesis testing under local differential privacy – Julian G. Gerstenberg, Goethe Universität Frankfurt, Institute for Mathematics, Germany: On the exchangeability theory and its applications in non-parametric statistics – Marija Cuparić, University of Belgrade, Serbia: Goodness-of-fit tests for randomly censored data – Charl Pretorius, University of the Free State: Bloemfontein, South Africa: Goodness-of-fit tests for multivariate α-stable distributions with application to MGARCH models Discussant: Bojana Milošević, University of Belgrade, Serbia The webinar is part of YoungStatS project of the Young Statisticians Europe initiative (FENStatS) supported by the Bernoulli Society for Mathematical Statistics and Probability and the Institute of Mathematical Statistics (IMS).