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Linear Programming-Based Estimators in Simple Linear Regression

Author

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  • Daniel Preve

    (Singapore Management University)

  • Marcelo Cunha Medeiros

    () (Department of Economics PUC-Rio)

Abstract

In this paper we introduce a linear programming estimator (LPE) for the slope parameter in a constrained linear regression model with a single regressor. The LPE is interesting because it can be superconsistent in the presence of an endogenous regressor and, hence, preferable to the ordinary least squares estimator (LSE). Two di erent cases are considered as we investigate the statistical properties of the LPE. In the rst case, the regressor is assumed to be xed in repeated samples. In the second, the regressor is stochastic and potentially endogenous. For both cases the strong consistency and exact nite-sample distribution of the LPE is established. Conditions under which the LPE is consistent in the presence of serially correlated, heteroskedastic errors are also given. Finally, we describe how the LPE can be extended to the case with multiple regressors and conjecture that the extended estimator is consistent under conditions analogous to the ones given herein. Finite-sample properties of the LPE and extended LPE in comparison to the LSE and instrumental variable estimator (IVE) are investigated in a simulation study. One advantage of the LPE is that it does not require an instrument.

Suggested Citation

  • Daniel Preve & Marcelo Cunha Medeiros, 2010. "Linear Programming-Based Estimators in Simple Linear Regression," Textos para discussão 567, Department of Economics PUC-Rio (Brazil).
  • Handle: RePEc:rio:texdis:567
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    References listed on IDEAS

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    1. Feigin, Paul D. & Resnick, Sidney I., 1994. "Limit distributions for linear programming time series estimators," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 135-165, June.
    2. B. Nielsen & N. Shephard, 2003. "Likelihood analysis of a first-order autoregressive model with exponential innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 337-344, May.
    3. Davis, Richard A. & McCormick, William P., 1989. "Estimation for first-order autoregressive processes with positive or bounded innovations," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 237-250, April.
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    Cited by:

    1. Naoto Kunitomo & Michael McAleer & Yoshihiko Nishiyama, 2010. "Moment Restriction-based Econometric Methods: An Overview," Working Papers in Economics 10/65, University of Canterbury, Department of Economics and Finance.
    2. Fengler, Matthias R. & Hin, Lin-Yee, 2015. "A simple and general approach to fitting the discount curve under no-arbitrage constraints," Finance Research Letters, Elsevier, vol. 15(C), pages 78-84.
    3. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.

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