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



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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    Cited by:

    1. Tae-Hwan Kim, 2005. "Asymptotic and Bayesian Confidence Intervals for Sharpe-Style Weights," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 315-343.
    2. 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).


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