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

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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.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d11/d1153.pdf
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    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).
    9. 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.

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