Generic results for establishing the asymptotic size of confidence sets and tests

This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic...

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Published inJournal of econometrics Vol. 218; no. 2; pp. 496 - 531
Main Authors Andrews, Donald W.K., Cheng, Xu, Guggenberger, Patrik
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.10.2020
Elsevier Science Publishers
Elsevier Sequoia S.A
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Abstract This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic is a discontinuous function of a parameter. The results are illustrated in several examples. These are: (i) the conditional likelihood ratio test of Moreira (2003) for linear instrumental variables models with instruments that may be weak, extended to the case of heteroskedastic errors; (ii) the grid bootstrap confidence interval of Hansen (1999) for the sum of the AR coefficients in a kth order autoregressive model with unknown innovation distribution, and (iii) the standard quasi-likelihood ratio test in a nonlinear regression model where identification is lost when the coefficient on the nonlinear regressor is zero. In addition, as a simple running example, we consider a two-sided equal-tailed CI for the AR coefficient in an AR(1) model, which is a simplified version of the CI in Andrews and Guggenberger (2014).
AbstractList This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic is a discontinuous function of a parameter. The results are illustrated in several examples. These are: (i) the conditional likelihood ratio test of Moreira (2003) for linear instrumental variables models with instruments that may be weak, extended to the case of heteroskedastic errors; (ii) the grid bootstrap confidence interval of Hansen (1999) for the sum of the AR coefficients in a kth order autoregressive model with unknown innovation distribution, and (iii) the standard quasi-likelihood ratio test in a nonlinear regression model where identification is lost when the coefficient on the nonlinear regressor is zero. In addition, as a simple running example, we consider a two-sided equal-tailed CI for the AR coefficient in an AR(1) model, which is a simplified version of the CI in Andrews and Guggenberger (2014).
This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic is a discontinuous function of a parameter. The results are illustrated in several examples. These are: (i) the conditional likelihood ratio test of Moreira (2003) for linear instrumental variables models with instruments that may be weak, extended to the case of heteroskedastic errors; (ii) the grid bootstrap confidence interval of Hansen (1999) for the sum of the AR coefficients in a kth order autoregressive model with unknown innovation distribution, and (iii) the standard quasi-likelihood ratio test in a nonlinear regression model where identification is lost when the coefficient on the nonlinear regressor is zero. In addition, as a simple running example, we consider a two-sided equal-tailed CI for the AR coefficient in an AR(1) model, which is a simplified version of the CI in Andrews and Guggenberger (2014).
This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic is a discontinuous function of a parameter.
Audience Academic
Author Andrews, Donald W.K.
Guggenberger, Patrik
Cheng, Xu
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Issue 2
Keywords Weak instruments
Asymptotic size
Confidence set
Weak identification
C10
C12
Test
Grid bootstrap
Inference
Autoregressive model
Identification
Uniform
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Snippet This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The...
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SubjectTerms Asymptotic methods
Asymptotic size
Autoregressive model
Bootstrap method
Confidence set
Estimating techniques
Grid bootstrap
Identification
Inference
Innovations
Nonlinear systems
Regression analysis
Test
Uniform
Weak identification
Weak instruments
Title Generic results for establishing the asymptotic size of confidence sets and tests
URI https://dx.doi.org/10.1016/j.jeconom.2020.04.027
https://www.proquest.com/docview/2480316776
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