Abstract
This paper presents recent developments in model selection and model averaging for parametric and nonparametric models. While there is extensive literature on model selection under parametric settings, we present recently developed results in the context of nonparametric models. In applications, estimation and inference are often conducted under the selected model without considering the uncertainty from the selection process. This often leads to inefficiency in results and misleading confidence intervals. Thus an alternative to model selection is model averaging where the estimated model is the weighted sum of all the submodels. This reduces model uncertainty. In recent years, there has been significant interest in model averaging and some important developments have taken place in this area. We present results for both the parametric and nonparametric cases. Some possible topics for future research are also indicated.
Highlights
Over the last several years many econometricians and statisticians have persistently devoted their efforts in finding various paths to the true model
We note that the traditional Akaike information criterion (AIC) and Bayesian information criterion (BIC) are based on least squares (LS), maximum likelihood (ML), or Bayesian principles, and the penalization is based on the l0 -norm for the parameters entering in the model, with the result penalization is proportional to the number of nonzero parameters
AIC is asymptotically efficient in the sense that it asymptotically selects the fitted candidate model which minimizes the MSE of prediction, but BIC is not asymptotically efficient
Summary
Over the last several years many econometricians and statisticians have persistently devoted their efforts in finding various paths to the true model. We note that the traditional AIC and BIC are based on least squares (LS), maximum likelihood (ML), or Bayesian principles, and the penalization is based on the l0 -norm for the parameters entering in the model, with the result penalization is proportional to the number of nonzero parameters Both AIC and BIC are variable selection procedures and do not provide estimators simultaneously. Related to “how”, or rather determining the unknown functional forms of econometric models, we use data based nonparametric procedures (e.g., kernel, smoothing spline, series approximation). These procedures help in dealing with the problems of bias and inconsistency in estimation and testing due to misspecifying functional forms Because of this recent developments on nonparametric model selection and model averaging have taken place.
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