This project consists of five areas of research. The first involves testing hypotheses with a restricted parameter space. This research will focus on the development of new tests that possess optimality properties and on the question of whether the likelihood ratio test is asymptotically admissible. The second area involves testing hypotheses when a nuisance parameter is present only under the alternative hypothesis. This research will also focus on developing new tests that have optimality properties for testing for random parameter variation. The third area involves estimation of the intercept of a semiparametric selection model. The forth area involves the estimation of nonlinear models with time trends. Research in this area will consider asymptotics for nonlinear estimators and models for data that exhibit deterministic and stochastic trends. The final area of research will focus on testing when a nuisance parameter is present only in parts of the null hypothesis.
