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December, 1983 Further Results on the Consistent Directions of Least Squares Estimators
Song-Gui Wang, C. F. J. Wu
Ann. Statist. 11(4): 1257-1262 (December, 1983). DOI: 10.1214/aos/1176346339


Wu (1980) defined the consistent directions of the least squares estimator in a linear model as the linear combinations of parameter estimates that are asymptotically consistent. For the polynomial regression model, a characterization of the space of consistent directions $S$ was obtained in terms of the convergence rates of the corresponding design sequence to its limit points. By employing a more general and yet simpler approach, we obtain here a similar result for any regression model with one independent variable and smooth regression function. When $f_i(x)$ is an extended Tchebycheff system, the above characterization is further refined and the consistency region $C$ is shown to be either the set of limit points of the design sequence or the whole real line.


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Song-Gui Wang. C. F. J. Wu. "Further Results on the Consistent Directions of Least Squares Estimators." Ann. Statist. 11 (4) 1257 - 1262, December, 1983.


Published: December, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0541.62048
MathSciNet: MR720271
Digital Object Identifier: 10.1214/aos/1176346339

Primary: 62J05
Secondary: 62E20

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 4 • December, 1983
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