2016/12/21 大纲 第8章非参数回归 参考：王星2014非参数统计chap8 ·核光滑回归 ·局部多项式回归 ·稳健回归 ·*K近邻回归 ·*正交序列回归 ·*B-Spline 1.非参数回归 Parametric partial parametric .The aim of a regression analysis is to producea reasonable analysis 8o公Po Y =m(X)+o(x.)s. example.a linear mode y=x/'B+E, i=1,…,N Ualle () aaceonpaonad y,=m(x,+E, 1=1,…,N 之h2 obe y=x,B+m:(3)+ i=1,…,N Motivation 光滑回归的基本原理 提供更丰富的用于表达变量关系的祝角，表达非线性结构 eto be made whou )=n() (2) 不需要在固定的参数形式下获得预测 Every smoothing method to be described is of the form(2). .It provides a tool for finding spurious observations by studying the W.(x)=K.(x-X)/i(x) (3) nfluence of isolated points 提供了一种发现异常观测并研究它可能影响的方法 where j(x)=nK(x-),and K(u)=hK(u/h) 面刷整案存在染大或两食对快大适行有您指鱼时。它的适 symmetric real function which integrates to. 12016/12/21 1 第8章 非参数回归 参考:王星2014 非参数统计chap8 王 星 办公电话:86-10-82500167 电子邮箱:wangxingwisdom@126.com 大 纲 • 核光滑回归 • 局部多项式回归 • 稳健回归 • *K近邻回归 • *正交序列回归 • *B-Spline Parametric & partial parametric 3 4 1.非参数回归 • The aim of a regression analysis is to produce a reasonable analysis to the unknown response function m, where for n data points ( ), the relationship can be modeled as • Unlike parametric approach where the function m is fully described by a finite set of parameters, nonparametric modeling accommodate a very flexible form of the regression curve. 超强适应的回归形式 Xi Yi , Y m(X ) , i 1, , n (1) i  i  i   ( ) ( ) Y m X X t t t t    5 Motivation • It provides a versatile method of exploring a general relationship between variables，can be used to test for nonlinearity. 提供更丰富的用于表达变量关系的视角,表达非线性结构 • It gives predictions of observations yet to be made without reference to a fixed parametric model 不需要在固定的参数形式下获得预测 • It provides a tool for finding spurious observations by studying the influence of isolated points 提供了一种发现异常观测并研究它可能影响的方法 • It constitutes a flexible method of substituting for missing values or interpolating between adjacent X-values 面对数据存在缺失或需要对缺失进行相邻插值时，它的适应 性很强 6 光滑回归的基本原理 • A reasonable approximation to the regression curve m(x) will be the mean of response variables near a point x. This local averaging procedure can be defined as Every smoothing method to be described is of the form (2). where , and . W (x) ni ( ) ( / ) 1 Kh u h K u h   Kernel smoothing describes the shape of the weight function by a density function K with a scale parameter that adjusts the size and the form of the weights near x. The kernel K is a continuous, bounded and symmetric real function which integrates to 1。 ˆ( ) ( ) (2) 1 1   n i ni Yi m x n W x ( ) (3) ˆ W (x) K (x X )/ f x hi  h  i h     n i h h Xi f x n K x 1 1 ( ) ( ) ˆ