Statistical tests based on empirical processes

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In most applications of statistics, dynamical stochastic models are assumed to satisfy certain hypotheses, mainly related to their probabilistic distribution. For example, in time series, random error terms (innovations) are often assumed to be independent and/or have a distribution belonging to some family of distributions. The general objective of the proposed research program is to further study empirical processes based on pseudo observations, which are transformations of data from the same sample, and use them to develop tests of lack-of-fit for models appearing mainly in actuarial science, econometrics, financial engineering and statistics. Since many important decisions rely on model assumptions, the proposed research project will mainly be used to develop new tools to verify rigorously these assumptions and therefore make better decisions.