Consider the standard non-linear regression model y_i=g(x_i,θ_o)+ε_i,i=1,...,n whereg(x,θ)is a continuous function on a bounded closed region X×Θ,θ_o is the unknown parametervector in θ■R_p,{x_1,x_2,...,x_...Consider the standard non-linear regression model y_i=g(x_i,θ_o)+ε_i,i=1,...,n whereg(x,θ)is a continuous function on a bounded closed region X×Θ,θ_o is the unknown parametervector in θ■R_p,{x_1,x_2,...,x_n}is a deterministic design of experiment and{ε_1,ε_2,...,ε_n}is asequence of independent random variables.This paper establishes the existences of M-estimates andthe asymptotic uniform linearity of M-scores in a family of non-linear regression models when theerrors are independent and identically distributed.This result is then used to obtain the asymptoticdistribution of a class of M-estimators for a large class of non-linear regression models.At the sametime,we point out that Theorem 2 of Wang(1995)(J.of Multivariate Analysis,vol.54,pp.227-238,Corrigenda.vol.55,p.350)is not correct.展开更多
基金This research was supported by the Natural science Foundation of china(Grant No.19831010 and grant No.39930160)and the Doctoral Foundation of China
文摘Consider the standard non-linear regression model y_i=g(x_i,θ_o)+ε_i,i=1,...,n whereg(x,θ)is a continuous function on a bounded closed region X×Θ,θ_o is the unknown parametervector in θ■R_p,{x_1,x_2,...,x_n}is a deterministic design of experiment and{ε_1,ε_2,...,ε_n}is asequence of independent random variables.This paper establishes the existences of M-estimates andthe asymptotic uniform linearity of M-scores in a family of non-linear regression models when theerrors are independent and identically distributed.This result is then used to obtain the asymptoticdistribution of a class of M-estimators for a large class of non-linear regression models.At the sametime,we point out that Theorem 2 of Wang(1995)(J.of Multivariate Analysis,vol.54,pp.227-238,Corrigenda.vol.55,p.350)is not correct.
