摘要
设(X,Y),(X_1,Y_1),…,(X_n,Y_n)为i.i.d R^d×{1,…,m}值的随机向量。Z^n=((X_1,Y_1),…,(X_n,Y_n))称作训练样本。(X,Y)分布未知,基于Z^n,X去判别Y属于非参数判别问题。Devroye[3]定义了一种核判别规则δ_n(X,Z^n),并在很弱的条件下证明了sum from n=1 to ∞∩~qP(L_n-R~*)>ε)<∞,其中L_n(δ_n,Z^n)为该判别的条件错判概率,R~*为Bayes判别的错判概率。本文在同样条件下,对同一判别规则,得到L_n(δ_n,Z^n)的指数收敛速度,较大地改进了Devroye的上述结果。
Let (X,Y),(X1,Y1),…,(Xn,Yn)be Rd× (1,…,M}-Valued i. i. d. random vectors Z?= ((X1 >Y1),…,(Xn,Yn)) is training sample. (X,Y) is distribation free> to discriminate Y based on Zn, Xbelongs to nonparametric discrimiuation. Devroye defined one kernel dis-crimination δn(X,Zn), and proved sum from n=I to ∞ nqp(Ln-R)>ε<∞ under some mild conditions,in which Ln (δn,Zn) is the conditimal error pr. , R is the Bayes error pr.In this paper, under the same condition, for the same δn(X,Zn), the exponenttia bound of Ln(δn,Z1n) is obtained which improves Devroye's result above.
