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Abstract

Any model is accompanied by a set of assumptions. These assumptions are based either on the underlying theory of the phenomena being modelled or on stylized statistical evidence, or more commonly on both. These, along with functional considerations such as variances being positive, often imply that values of some parameters characterizing a model are restricted to one side of a point in the parameter space. This information can be used to improve the power of hypothesis testing procedures. In this paper, we discuss some recent developments on testing against such one-sided alternative hypotheses with particular emphasis on the econometrics literature. The focus is on two main approaches: that based on maximum likelihood estimation and that based on local power optimization facilitated by the generalized Neyman-Pearson lemma. Both single parameter and multi-parameter testing problems are considered.

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