Least Square Method for Concave Regression

• Main Authors: Kuo-Lung Wang, 王國龍
• Other Authors: Chi-Chung Wen
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/14849511950359715572

碩士 === 淡江大學 === 數學學系碩士班 === 98 === Search for a simple, smooth and efficient estimator of a smooth concave regression function is of considerable interest. In this thesis, we describe a least square method for concave regression in which the regression function is modeled by the Bernstein polynomial. We employ the Akaike’s information criterion to determine the degree of Bernstein polynomial, propose a penalty function method based algorithm to compute estimate and provide a pointwise confidence interval estimator and a prediction interval band for regression function. The success of this method is demonstrated in simulation studies and in an analysis of real data.