Statistical inference about a scalar parameter is often performed using the two-sided ttest.
In extremum problems, where the estimator satises the restrictions on the parameter
space - such as the nonnegativity of a variance parameter -, the test suers from size distortions
when the true parameter vector is near or at the boundary of the parameter space.
Nevertheless, the two-sided t-test continues to be used when estimates are found to be close
to the boundary. This can be attributed to a lack of inference procedures that appropriately
account for boundary eects on the asymptotic distribution of the estimator. To address this
issue, we propose an estimator that is asymptotically normally distributed, even when the
true parameter vector is near or at the boundary, and the objective function is not dened
outside the parameter space. The novel estimator allows the implementation of several existing
testing procedures and a new test based on the Conditional Likelihood Ratio statistic
(CLR). Compared to the existing procedures, the new test is easy to implement and has
good power properties. Moreover, it oers power advantages over the two-sided t-test, when
the latter controls size. We also show the test to be admissible when inference is performed
with respect to a scalar parameter. We apply the test to the random coecients logit model
using data on the European car market and nd more evidence of heterogeneity in consumer
preferences than suggested by the two-sided t-test.