I am interesting in answering fundamental research questions in Statistics and Machine Learning, using tools in Probability and Stochastic Processes, as well as in Applied Statistics and various models in Medicine and Biostatistics. More precisely, I focus on nonparametric asymptotic hypothesis testing using tools from Stochastic Processes; inference for evolutionary clusters of increasing size, with limit theorems for martingale transforms; estimation for models with measurement errors, as well as model selection methods for mixed models.