| Summary: | 碩士 === 國立交通大學 === 統計學類 === 86 === Consider the problem of estimating an unknown function that
is smooth expect for some change-points, where discontinuities
occur on either the function or its derivatives. In this paper,
we propose estimators for the location and jumpsize of the
discontinuity, respectively, based on one-sided local polynomial
regression smoothers. The asymptotic normality is established
for both the change-point and jump size estimators under
regularily conditions. Estimators of the mean function and its
derivatives are also proposed. The boundary behaviors of these
estimators are investigated, including the boundary regions and
neighborhoodsof the change-point. It is found that the resulting
estimators are free of the boundary effects. Unfortunately,
there is a change-point effect due to the errorsfrom the
estimation of the location and the jump size of the change-
point. In addition, we give some theoretical reasons to
distinguish cases between p-nu oddand p-nu even, where p is the
order of the local polynomial and nu is the order of the
discontinuities of the fuction at the change-point. Finite
sample properties are studied via simulations.
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