A Comparison of james–sten regression with least squares in the pitman nearness sense (original) (raw)
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American Journal of Mathematical and Management Sciences, 2001
Employing large sample asymptotic theory, an asymptotic approximation for the Pitman closeness probability is derived and a comparison of the least squares and Stein-rule estimators is made when the aim is to estimate the coefficients in a linear regression model. Since the disturbances are assumed to be not necessarily normal, the Edgeworth expansion is utilized to obtain an approximation for the characteristic function from the cumulant generating function.
Pitman nearness in statistical estimation
Computational Statistics & Data Analysis, 1991
In 1981 C Radhakrlshna Rao revived Interest m Pltman's nearness crlterlon through a mynad of examples that arlse out of diverse fields m estimation theory Among the unsolved problems cited m the literature m this area, IS the comparison of the classical least squares and the inverse least squares m the regresslon context Herem the classical least squares and the mverse least squares estimators for the slope parameter m a simple linear regression model are compared using Pltman's measure of closeness as a crlterlon It IS shown that the Inverse estimator IS madmlsslble with respect to the classical estimator The results are applied to a slmdar estlmatlon problem m cahbratlon Keywords Pltman nearness, Cahbratlon, Rao's noncentral F. Rao's phenomenon J P Keatmg et al / Pttman nearness tn statistical esttmatton 11 Dyer, D and Keatmg, J.P (1981), "On the Relative Behavior of Estimators of the Charactenstlc Life m the Exponential Falure Model," Communrcatrons rn Statistics, AlO, 489-501
Applied and Computational Mathematics
Isoperimetric, Milman reverse, Hilbert, Widder, Fan-Taussky-Todd, Landau, and Fortuin-Kasteleyn-Ginibre (FKG) inequalities in n dimensions in investigations of multidimensional estimators support the use of James-Stein estimator against classical least squares as applied to Cumulant Analysis, Associate Random Variables, and Time Series Analysis.
Asymptotic mean squared error of constrained James–Stein estimators
Journal of Statistical Planning and Inference, 2004
In this paper, we consider the asymptotic expansion of the MSE of constrained James-Stein estimators. We provide an estimator of the MSE which is asymptotically valid upto O(m −1 ). A simulation study is undertaken to evaluate the performance of these estimators.
Performance of the 2SHI estimator under the generalised pitman nearness criterion
Communications in Statistics - Theory and Methods, 1997
The paper considers an extension of Tran Van Hoa's family of 2SHI (two stage hierarchical information) estimators for the coefficient vector of a linear regression model and derives the conditions for the dominance of the 2SHI estimator over the OLS and Stein rule estimators under a Generalized Pitman Nearness (GPN) criterion when the disturbance variable is small. † This work was carried out during the second author's visit to the Department of Economics, University of Wollongong, as a Visiting Lecturer. The financial support and research facilities from the Department are greatly appreciated.