IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1153.html
   My bibliography  Save this paper

Estimation When a Parameter Is on a Boundary: Theory and Applications

Author

Abstract

This paper establishes the asymptotic distribution of extremum estimators when the true parameter lies on the boundary of the parameter space. The boundary may be linear, curved, and/or kinked. The asymptotic distribution is a function of a multivariate normal distribution in models without stochastic trends and a function of a multivariate Brownian motion in models with stochastic trends. The results apply to a wide variety of estimators and models. Examples treated explicitly in the paper are: (1) quasi-ML estimation of a random coefficients regression model with some coefficient variances equal to zero, (2) LS estimation of a regression model with nonlinear equality and/or inequality restrictions on the parameters and iid regressors, (3) LS estimation of an augmented Dickey-Fuller regression with unit root and time trend parameters on the boundary of the parameter space, (4) method of simulated moments estimation of a multinomial discrete response model with some random coefficient variances equal to zero, some random effect variances equal to zero, or some measurement error variances equal to zero, (5) quasi-ML estimation of a GARCH(1,q*) or IGARCH(1,q*) model with some GARCH MA parameters equal to zero, (6) semiparametric LS estimation of a partially linear regression model with nonlinear equality and/or inequality restrictions on the parameters, and (7) LS estimation of a regression model with nonlinear equality and/or inequality restrictions on the parameters and integrated regressors.

Suggested Citation

  • Donald W.K. Andrews, 1997. "Estimation When a Parameter Is on a Boundary: Theory and Applications," Cowles Foundation Discussion Papers 1153, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1153
    Note: CFP 988.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d11/d1153.pdf
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gregory Fletcher Cox, 2024. "A Simple and Adaptive Confidence Interval when Nuisance Parameters Satisfy an Inequality," Papers 2409.09962, arXiv.org.
    2. Yunmi Kim & Douglas Stone & Tae-Hwan Kim, 2021. "Testing for structural breaks in return-based style regression models," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 35(1), pages 61-76, March.
    3. Marine Carrasco & N’Golo Koné, 2024. "Test for Trading Costs Effect in a Portfolio Selection Problem with Recursive Utility," Journal of Financial Econometrics, Oxford University Press, vol. 22(4), pages 908-953.
    4. Tae-Hwan Kim, 2005. "Asymptotic and Bayesian Confidence Intervals for Sharpe-Style Weights," Journal of Financial Econometrics, Oxford University Press, vol. 3(3), pages 315-343.
    5. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    6. Dimitriadis, Timo & Liu, Xiaochun & Schnaitmann, Julie, 2020. "Encompassing tests for value at risk and expected shortfall multi-step forecasts based on inference on the boundary," Hohenheim Discussion Papers in Business, Economics and Social Sciences 11-2020, University of Hohenheim, Faculty of Business, Economics and Social Sciences.
    7. Fan, Yanqin & Shi, Xuetao, 2023. "Wald, QLR, and score tests when parameters are subject to linear inequality constraints," Journal of Econometrics, Elsevier, vol. 235(2), pages 2005-2026.
    8. Hilmer, Christiana E. & Holt, Matthew T., 2000. "A Comparison Of Resampling Techniques When Parameters Are On A Boundary: The Bootstrap, Subsample Bootstrap, And Subsample Jackknife," 2000 Annual meeting, July 30-August 2, Tampa, FL 21810, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1153. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.