The next RITM Economics Seminar will take place on Monday 10 February, in room Gaudemet (Jean Monnet – 54 boulevard Desgranges – 92330 Sceaux) from 11:00 to 12:00. Yannick Guyonvarch (CREST-ENSAE) will present « On the construction of nonasymptotic confidence intervals in linear models » (with Alexis Derumigny (University of Twente) et Lucas Girard (CREST)).
Abstract : « We are concerned with constructing nonasymptotic confidence intervals (CIs) for the individual coefficients of a linear regression model, i.e CIs that have the desired level for any given sample size. The existing tools to conduct nonasymptotic inference either rely on the normality of the error term or the independence between the error term and the observed covariates of the model. Those assumptions may however be restrictive in economic applications : normality rules out models with skewed or fat-tailed idiosyncratic shocks while independence does not allow for heteroskedastic shocks. Our contribution is twofold. First, when there is no endogeneity, we propose a novel CI close in spirit to the one based on the Wald statistic (Wald CI). Unlike the latter which has only asymptotic validity, our CI is valid for any sample size larger than two if the distribution of the errors conditional on covariates has bounded kurtosis and fourth moment. Furthermore, our CI has the same asymptotic length as the Wald CI, which is known to be optimal. Second, when one of the covariates is endogenous and there is exactly one excluded instrument, we propose a modification of the asymptotic Anderson-Rubin CI (1949) that is valid for any sample size under analogous conditions to the exogenous case. Our CI inherits the following appealing property of the Anderson-Rubin construction : inference remains valid even when the excluded instrument is uncorrelated with the endogenous variable. Our work builds upon a long-standing statistics literature that was crucially influenced by Berry (1941) and Esseen (1942). We also discuss possible improvements of our results when we impose that errors be symmetrically distributed conditional on covariates. We finally investigate the practical performance of our CIs in small-sample simulation studies.»