Nearly Optimal Tests when a Nuisance Parameter is Present Under the Null Hypothesis∗
نویسندگان
چکیده
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. JEL classification: C12; C21; C22
منابع مشابه
Comparison between Frequentist Test and Bayesian Test to Variance Normal in the Presence of Nuisance Parameter: One-sided and Two-sided Hypothesis
This article is concerned with the comparison P-value and Bayesian measure for the variance of Normal distribution with mean as nuisance paramete. Firstly, the P-value of null hypothesis is compared with the posterior probability when we used a fixed prior distribution and the sample size increases. In second stage the P-value is compared with the lower bound of posterior probability when the ...
متن کاملOPTIMAL TESTS WHEN A NUISANCE PARAMETER IS PRESENT ONLY UNDER THE ALTERNATIVE by
1994 The copyright to this Article is held by the Econometric Society. It may be downloaded, printed and reproduced only for educational or research purposes, including use in course packs. No downloading or copying may be done for any commercial purpose without the explicit permission of the Econometric Society. For such commercial purposes contact the Office of the Econometric Society (contac...
متن کاملTesting Conditional Independence via Empirical Likelihood
We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis an...
متن کاملPoint optimal testing: A survey of the post 1987 literature
In the absence of uniformly most powerful (UMP) tests or uniformly most powerful invariant (UMPI) tests, King (1987c) suggested the use of Point Optimal (PO) tests, which are most powerful at a chosen point under the alternative hypothesis. This paper surveys the literature and major developments on point optimal testing since 1987 and suggests some areas for future research. Topics include tes...
متن کاملUnit Root Tests for Time Series with a Structural Break When the Break Point Is Known
Unit root tests for time series with level shifts are considered. The level shift is assumed to occur at a known time point. In contrast to some other proposals the level shift is modeled as part of the intercept term of the stationary component of the data generation process which is separated from the unit root component. In this framework simple shift functions result in a smooth transition ...
متن کامل