Firms and Markets Seminar
We propose confidence intervals for the coefficients in a linear regression model that are valid with i.i.d observations for every sample size larger than two. We do not resort to the assumption that the errors are normally distributed to get our result. Our construction only requires moment restrictions on the data generating process (DGP) to allow for the use of Berry-Esseen-type arguments as well as so-called concentration inequalities for random variables and random matrices. We exhibit a lower bound on the confidence level they achieve in finite samples and we show that they are asymptotically of the same length as the confidence intervals based on asymptotic normality. We also discuss the issue of uniformity over classes of DGPs and how to improve our results under more stringent moment conditions. This work builds upon a very large literature that was crucially influenced by Berry (1941) and Esseen (1942).
Please note that this is an early-stage project.