Exact and nonparametric inference in regression and structural models in the presence of heteroskedasticity of arbitrary form.

Summary This thesis develops a finite sample exact inference system in regression and structural models without imposing any parametric assumption on the error distribution. First, we study the construction of tests and confidence regions in a linear regression on the median. The statistics based on the aligned residual signs have a known and simulatable distribution, which allows us to construct a valid simultaneous inference procedure regardless of the sample size. Next, we associate an estimator and study additional inference tools such as the p-value function that gives a confidence level to each tested parameter value. Finally, we extend the procedure to non-linear structural models, by adapting the sign pivotality to the instrumental model. The resulting exact tests do not depend on the degree of identification and are valid in the presence of weak instruments.