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SUMMARY It is known that iterative weighted least squares (IWLS) does not merely yield a convenient way of fitting the general class of regression models considered by Green but is also a useful means of unifying techniques of model checking. However, an extension of these results to models containing nuisance or incidental parameters has made little progress beyond some special cases. Unfortunately, regression models with nuisance parameters that are not dispersion…

非线性估计方程的求解AI 解读

SUMMARY In this paper we consider the numerical computation of a vector parameter estimate θ^ which is a root of a system of unbiased non-linear estimation equations. A sequence {θ (r)} is constructed which converges with a probability approaching 1 to θ^ from any starting value θ (0). Unlike Newton-type algorithms, the θ (r) do not involve matrices of partial derivatives. Furthermore it can be shown that θ(r)−θ^ is of the order Op(n – r/2) so that great accuracy is achieved…

异方差线性模型中的参数估计AI 解读

SUMMARY This paper deals with linear regression models with non-homogeneous error variances. The common situation where the error variance is a smooth function of the values of the regressor variables is considered. The error variance function is represented by a function of known form, but its expression involves the vector of unknown regression coefficients β and an additional vector parameter θ. Estimation of β by iterative weighted least squares (IWLS) therefore also…

误分类条件下的子群均值估计AI 解读

SUMMARY The present paper considers the estimation of subgroup means in the presence of misclassification errors in allocating individuals to the subgroups. A simple non-iterative estimator resulting from modifying Selen's (1986) estimator is studied when the probabilities of misclassification are independently estimated. In contrast to Selen (1986), an explicit expression for the covariance matrix of the suggested estimator is obtained using special matrix products and…

关于多项式函数关系模型AI 解读

SUMMARY A method for obtaining consistent estimators of the coefficients in a polynomial functional relationship model with normal errors is proposed when the error covariance matrix is either completely known or known up to a proportionality factor. For quadratic functional relationships with possibly non-normal errors, we present a consistent estimator when the error covariance matrix is known. A large sample test of the quadratic against the linear functional relationship…

论 Sprent 的广义最小二乘估计量AI 解读

Summary This paper studies the asymptotic properties of Sprent's (1966) generalized least-squares estimator of the slope parameter in a functional relationship model which allows errors at different data points be correlated. Consistency is established and the asymptotic variance derived. When the Joint distribution of the errors is normal, in which case Sprent's estimator coincides with the maximum likelihood estimator, the asymptotic variance formula is further simplified…