Least Squared Simulated Errors

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