Printed in Great Britain Parameter-based asymptotics

In certain cases statistical methods based on standard maximum likelihood asymptotics become valid as the true parameter value approaches a boundary of the parameter space. Examples are given which motivate a general parameter-based asymptotic theory, and a result is obtained which covers such situations. Of particular interest are applications to stochastic process models. Some key words: Inference for stochastic processes; Maximum likelihood estimation; Parameter-based asymptotics. 1