### Abstract

This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish an upper bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two independent Gaussian samples from populations with potentially different variances; inference about the break date in structural break models with moderate break magnitude; predictability tests when the regressor is highly persistent; inference about an interval identified parameter; and inference about a linear regression coefficient when the necessity of a control is in doubt.

Original language | English (US) |
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Pages (from-to) | 771-811 |

Number of pages | 41 |

Journal | Econometrica |

Volume | 83 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2015 |

### All Science Journal Classification (ASJC) codes

- Economics and Econometrics

### Keywords

- Least favorable distribution
- composite hypothesis
- maximin tests

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## Cite this

*Econometrica*,

*83*(2), 771-811. https://doi.org/10.3982/ECTA10535