This paper establishes the asymptotic distribution of extremum estimators when the true parameter lies on the boundary of the parameter space. The boundary may be linear, curved, and/or kinked. Typically the asymptotic distribution is a function of a multivariate normal distribution in models without stochastic trends and a function of a multivariate Brownian motion in models with stochastic trends. The results apply to a wide variety of estimators and models. Examples treated in the paper are: (1) quasi-ML estimation of a random coefficients regression model with some coefficient variances equal to zero and (2) LS estimation of an augmented Dickey-Fuller regression with unit root and time trend parameters on the boundary of the parameter space.
