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Least Squared Simulated Errors

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  • Peter J. Veazie
  • Shubing Cai

Abstract

Estimation by minimizing the sum of squared residuals is a common method for parameters of regression functions; however, regression functions are not always known or of interest. Maximizing the likelihood function is an alternative if a distribution can be properly specified. However, cases can arise in which a regression function is not known, no additional moment conditions are indicated, and we have a distribution for the random quantities, but maximum likelihood estimation is difficult to implement. In this article, we present the least squared simulated errors (LSSE) estimator for such cases. The conditions for consistency and asymptotic normality are given. Finite sample properties are investigated via Monte Carlo experiments on two examples. Results suggest LSSE can perform well in finite samples. We discuss the estimator’s limitations and conclude that the estimator is a viable option. We recommend Monte Carlo investigation of any given model to judge bias for a particular finite sample size of interest and discern whether asymptotic approximations or resampling techniques are preferable for the construction of tests or confidence intervals.

Suggested Citation

  • Peter J. Veazie & Shubing Cai, 2015. "Least Squared Simulated Errors," SAGE Open, , vol. 5(1), pages 21582440155, March.
    • Handle: RePEc:sae:sagope:v:5:y:2015:i:1:p:2158244015575555
    DOI: 10.1177/2158244015575555
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    References listed on IDEAS

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    3. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
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    7. Gourieroux, Christian & Monfort, Alain, 1993. "Simulation-based inference : A survey with special reference to panel data models," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 5-33, September.
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