Heteroscedastic errors in a linear functional relationship

摘要: SUMMARY We consider the estimation of structural parameters in a multivariate linear func- tional relationship when error variances and covariances are not necessarily homogeneous. Estimators obtained as roots system nonlinear equations an iterative algorithm is briefly described for finding numerical solutions system. Asymptotic properties estimators studied particular estimate asymptotic covariance matrix derived. The functional relationships has been extensively investigated literature. Yet many models assumed that errors indepen- dently identically distributed. Barnett (1970) discussed application to medical example which assumption homogeneous unrealistic. In present paper following model will be considered. Suppose two unobservable nonstochastic variables m i dimensions re- spectively p q connected by underlying = + B. B unknown estimated based on n independent pairs observations (xi, yr) 1, ..., n, with Xi ~i31, yi=q+e +~+i where (5k, si) zero mean f2i. Here f2i either all known or they given functions same parameter ? 2, it noted different approaches, including Morton's (1981) generalized likelihood procedure, lead estimating a, 0. Consistency normality derived established under certain conditions also 3. These satisfied corresponding nonidentifiable. An proposed solving numerically.