Title: Statistical functionals of residuals
Authors: Vanessa Berenguer Rico - University of Oxford (United Kingdom) [presenting]
Bent Nielsen - University of Oxford (United Kingdom)
Abstract: The analysis of residuals is central in statistical modelling. This is often conducted using specification tests that involve statistical functionals of residuals. We provide a general theoretical framework to systematically analyse the asymptotic properties of a wide class of residual-based specification tests. The framework is built using empirical processes techniques and it is general enough to handle standard least squares regressions as well as robust estimation procedures in models that include stationary and non-stationary regressors. The theoretical framework is then applied to study the asymptotic properties of some well-known specification tests, i.e., normality test based on cumulants, Kolmogorov-Smirnov statistics, or White heteroskedasticity test. These are analysed in least squares and robust regression contexts.