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Essays on Semiparametric Ridge-Type Shrinkage Estimation, Model Averaging and Nonparametric Panel Data Model Estimation


This dissertation is composed with 4 essays. They explore modelling uncertainty following two major directions. The former 2 contains topics on ordinary and general ridge-type shrinkage estimation developed from model averaging and kernel density estimation. The third one critically reviews recent literature in the areas of model averaging and model selection both parametrically and nonparametrically and proposes topics for future work. The last one focuses on nonparametric panel data estimation with random effects. In chapter 2, ordinary ridge-type shrinkage estimation is extensively studied, where a class of well-behaved ordinary ridge-type semiparametric estimators is proposed. Monte Carlo simulations, theoretical derivations, as well as empirical out-of-sample forecasts are all investigated to prove their usefulness in reducing mean squared errors, i.e. risks. Chapter 3 develops the works in Chapter 2 to the general ridge regressions. By connecting general ridge regression with kernel density estimation, an asymptotically optimal semiparametric ridge-type estimator is built. By connecting general ridge regression with model averaging, a class of model averaging ridge-type estimators are obtained. These estimators are observed to have different improvements upon the feasible general ridge estimators when model uncertainties, i.e., the error variances are different. To encourage better understanding on model averaging and model selection, Chapter 4 gives a comprehensive literature review and analysis on these topics from a frequentist's point of view. Parametric and nonparametric procedures in the recent developments are explored. Chapter 5 starts investigating panel data estimation by introducing nonparametrics in the picture. The proposed two-stage estimator shows good behaviors in Monte Carlo simulation. In addition, illustrative empirical examples in health economics and environmental economics are also introduced.

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