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Non-Standard Tests through a Composite Null and Alternative in Point-Identified Parameters

Author

Listed:
  • Hahn Jinyong

    ()

  • Ridder Geert

    (Department of Economics, Bunche Hall, UCLA, Los Angeles, CA 90095, USA)

Abstract

We propose a new approach to statistical inference on parameters that depend on population parameters in a non-standard way. As examples we consider a parameter that is interval identified and a parameter that is the maximum (or minimum) of population parameters. In both examples we transform the inference problem into a test of a composite null against a composite alternative hypothesis involving point identified population parameters. We use standard tools in this testing problem. This setup substantially simplifies the conceptual basis of the inference problem. By inverting the Likelihood Ratio test statistic for the composite null and composite alternative inference problem, we obtain a closed form expression for the confidence interval that does not require any tuning parameter and is uniformly valid. We use our method to derive a confidence interval for a regression coefficient in a multiple linear regression with an interval censored dependent variable.

Suggested Citation

  • Hahn Jinyong & Ridder Geert, 2015. "Non-Standard Tests through a Composite Null and Alternative in Point-Identified Parameters," Journal of Econometric Methods, De Gruyter, vol. 4(1), pages 1-28, January.
  • Handle: RePEc:bpj:jecome:v:4:y:2015:i:1:p:28:n:8
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    References listed on IDEAS

    as
    1. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    2. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
    3. Morales, Eduardo & Sheu, Gloria & Zahler, Andrés, 2011. "Gravity and extended gravity: estimating a structural model of export entry," MPRA Paper 30311, University Library of Munich, Germany.
    4. Fan, Yanqin & Park, Sang Soo, 2010. "Confidence sets for some partially identified parameters," MPRA Paper 37149, University Library of Munich, Germany.
    5. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    Full references (including those not matched with items on IDEAS)

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