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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.
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.