Edge-preserving smoothers for nonparametric regression

• Main Authors: Szu-Chin Lin, 林賜欽
• Other Authors: Jyh-Shang Wu
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/15978517840298329955

碩士 === 淡江大學 === 數學學系 === 88 === Abstract: In the nonparametric regression model, when the regression curve is jump discontinuity, the bias of kernel estimator will be when we to estimate , belongs to . Hence the estimator will be not consistent in the interval. So, if we use integrated mean square error ( IMSE ) to comment the estimator , the best convergent rate will be from become to . The convergent rate is worse than the integrated mean square error of the kernel estimator that has no jump points. In this article, we propose a new estimator that we called “ robust kernel estimator”. For the new estimator, the area which have edge effect can be descended to . The convergent rate of IMSE will be not influenced by the jump points. The rate still remains as the same as no jump points occur. The rate will be still , when the smoothing parameter is chose as , is some constant.In the first section, we review the parametric and nonparametric regression,and brief introduce the kernel estimator. In the second section, we introduce the edge effect and generalized edge effect. In the third section, we propose a new method that is called “ robust kernel estimator” to deal with the effect of jump points. We give the theoretical result in the fourth section, and prove it in the fifth section. Finally, we give the simulation result in the sixth section.