The first chapter of this dissertation introduces the generalized minimum contrast estimator (GMC) with nonsmooth moment functions and studies its asymptotic properties under mild conditions. A Chi- square test based on GMC is discussed. The duality between the GMC and the Generalized Empirical Likelihood Estimator (GEL) is interpreted from both a computational perspective and geometric perspective. The second chapter investigates a Bayesian approach to calculating the GMC. By updating the concerned parameters and nuisance parameters alternatively, this approach can converge quickly and can be implemented easily. Its performance is compared to existing methods based on both just-identified conditions and over-identified conditions. The third chapter employs a partial linear model (PL) and geographically weighted regression (GWR) to estimate housing prices. These two semiparametric models provide flexible consideration of spatial heterogeneity and spatial correlation. Their performance is compared through various simulation experiments. An empirical study of the housing market in Connecticut is also implemented.

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