On Sprent's Generalized Least-Squares Estimator
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1983 · Volume 45 · Issue 3
DOI: 10.1111/j.2517-6161.1983.tb01265.x
Abstract
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 and the limiting distribution of the estimator is also shown to be normal. The variance expression obtained under the normality assumption differs from that of Dolby (1972) derived by inverting the information matrix, and the latter procedure is known to be generally invalid in functional relationship problems due to the presence of incidental parameters (Patefield, 1978). An estimator of the asymptotic variance is also suggested.
Keywords
asymptotic properties, functional relationship, maximum likelihood estimation, sprent's generalized least-squares estimator
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