The influence function in the errors in variables problem
The paper deals with the problem of variance estimation of some parameter vector estimators in the model \(z_ i=u_ i+e_ i\), \(i=1,...,n\), where the components of \(u_ i\) are linearly related: \(u_{2i}=\alpha +\beta u_{1i}\); \(u_ i\), \(e_ i\) are i.i.d. variables and are independent; the ratio of error variances is known; the common distribution of \(z_ i\) admits fourth order moments. The influence function of an estimator is calculated and used to calculate its asymptotic covariance matrix. The connection with estimation in the linear regression model is considered. The behaviour of some classical estimators is investigated by Monte Carlo methods. A numerical example taken from the literature is used to illustrate the rôle of the influence function in detection of influential observations.
scientific article; zbMATH DE number 3890557