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Trinity tests of functions for conditional moment models

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  • Tao, Jing

Abstract

This paper considers conditional moment models where the parameters of interest include both finite-dimensional parameters and unknown functions. We propose sup-Wald, sup-quasi-likelihood ratio and sup-Lagrange multiplier statistics for testing functionals restrictions uniformly over the support for both finite and infinite dimensional components of the parameters. The trinity of three statistics holds because they are asymptotically equivalent and can be strongly approximated by a sequence of chi-squared processes. Based on these results, we can, for instance, construct confidence intervals and uniform confidence bands for the unknown functions, the partial derivatives of the unknown functions and the functional combinations of the two parameters.

Suggested Citation

  • Tao, Jing, 2020. "Trinity tests of functions for conditional moment models," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:jmvana:v:178:y:2020:i:c:s0047259x18306699
    DOI: 10.1016/j.jmva.2020.104604
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    References listed on IDEAS

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    1. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    2. Xiaohong Chen & Timothy M. Christensen, 2018. "Optimal sup‐norm rates and uniform inference on nonlinear functionals of nonparametric IV regression," Quantitative Economics, Econometric Society, vol. 9(1), pages 39-84, March.
    3. Horowitz, Joel L. & Lee, Sokbae, 2012. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," Journal of Econometrics, Elsevier, vol. 168(2), pages 175-188.
    4. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    5. Freyberger, Joachim & Horowitz, Joel L., 2015. "Identification and shape restrictions in nonparametric instrumental variables estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 41-53.
    6. Sueishi, Naoya, 2017. "A Note On Generalized Empirical Likelihood Estimation Of Semiparametric Conditional Moment Restriction Models," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1242-1258, October.
    7. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    8. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
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    Cited by:

    1. Christoph Breunig & Xiaohong Chen, 2020. "Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models," Cowles Foundation Discussion Papers 2238R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.

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