Another view of the Kuks–Olman estimator

A surprising property of uniformly best linear affine estimation in linear regression when prior information is fuzzy

“…To be more precise, Arnold and Stahlecker (2000) derived an estimator being minimax in the class of all linear affine estimators. Wilczyń ski (2005) proved that this estimator is minimax not only among all linear affine estimators but also in the class of all estimators.…”

“…Wilczyń ski (2005) proved that this estimator is minimax not only among all linear affine estimators but also in the class of all estimators. In the relative squared error approach proposed by Arnold and Stahlecker (2000), the quadratic form of the denominator is presupposed to be p.d. Subsequently, this assumption was weakened; the denominator of the relative squared error in Arnold and Stahlecker (2002) is merely assumed to be n.n.d.…”

“…The research about this property was inspired by Wilczyń ski (2005). In that paper, a minimax result of Arnold and Stahlecker (2000) on a relative squared error approach to linear regression analysis is largely generalized. Let us start with the remark that the equation…”

Covariance structure associated with an equality between two general ridge estimators

“…Moreover, they are linearly complete. For other properties of general ridge estimator, see, for example, Arnold and Stahlecker (2000), Gross (1998) and Groß and Markiewicz (2004). On the other hand, it is also well-known that there are some cases in which two linear unbiased estimators coincide with each other.…”

Adaptive Unified Biased Estimators of Parameters in Linear Model

“…However the least squares estimators are not robust for estimating β especially with multicollinearity and ill-conditioned design matrix. This problem leads to the development of the Stein [17] estimator, the ridge regression estimator [9] and the principal components estimator (see [7,16,22]), Panopoulos [15] did some comparison among several ridge estimators, Donatos and Michailidis [5,6] studied some small sample properties of ridge estimators and made a comparison with the least squares estimator, Choi and Hall [4] used the idea of ridge estimator in dealing with density estimation, Arslan and Billor [1] as well as Arnold and Stahlecker [3] investigated the ridge type estimators, Fu [8] further studied ridge estimator and applied it to a real data analysis, Inoue [10,11] studied the relative efficiency of double f -class generalized ridge and some related ridge estimators. For principal components estimators, Lin and Wei [13] studied the small sample properties of the principal components and Walker [20] Manuscript received January 20, 2003 investigated the influence diagnostics for fractional principal components estimators.…”