This collection of papers delivered at the fifth international Symposium in Economic Theory and Econometrics in 1988 is devoted to recent advances in the estimation and testing of models that impose relatively weak restrictions on the stochastic behavior of data. Particularly in highly nonlinear models, empirical results are very sensitive to the choice of the parametric form of the distribution of the observable variables, and often nonparametric and semiparametric models are a preferable alternative. Methods and applications that do not require strong parametric assumptions for their validity, that are based on kernels and on series expansions, and methods for independent and dependent observations, are investigated and developed in these essays by renowned econometricians.