Change-Point Estimation by Local Polynomial Smoothing

• Main Authors: Lin, Pei-Rung, 林佩蓉
• Other Authors: Jyh-Jen Horng Shiau
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/40324249922899655630

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.