A Coordinate Measuring Machine (CMM) is a computer-controlled device that uses a probe to obtain measurements on a manufactured part's surface. In the process of collecting, analyzing and...
: A linear model based on the spherical coordinate system is employed for fitting a spherical surface to a data set obtained by a coordinate measuring machine (CMM). In practice, measurement data may...
Consistent Directions of the Least Squares Estimators in Linear Models. (2002)
The consistent directions of the least squares estimators in a linear model are defined to be the linear combinations of parameter estimates that are asympotically consistent. When the design...
Another look at the naive estimator in a regression model
naive LS estimator, general ridge estimator, mean square error matrix,
Constrained Kantorovich inequalities and relative efficiency of least squares
This paper establishes a type of Kantorovich inequality subject to some constraints and obtains some lower bounds for the relative efficiency of the least squares. These lower bounds can be much...
A new generalized p-value for ANOVA under heteroscedasticity
For the problem of comparing the means of k populations with unequal population variances, a new generalized test variable is defined and the generalized p-value based on this generalized test...
A GIC rule for assessing data transformation in regression
Ip, Wai Cheung, Wong, Heung, Wang, Song-Gui
The functional form used in regression may be generalized by the Box-Cox transformation. We adopt the generalized information criterion (GIC)Â approach to determine a need for Box-Cox (J. Roy....
A stratified sampling model in spherical feature inspection using coordinate measuring machines
Fang, Kai-Tai, Wang, Song-Gui, Wei, Gang
A coordinate measuring machine (CMM) is a computer-controlled device that uses a probe to obtain measurements on a manufactured part's surface. In the process of collecting, analyzing and...
On ordinary least-squares methods for sample surveys
Wang, Song-Gui, Chow, Shein-Chung, Tse, Siu-Keung
The performance of the ordinary least-squares (LS) method for two-stage sampling in regression analysis is studied. It is shown that the best linear unbiased estimator (BLUE) can be approximated by a...
A note on adaptive generalized ridge regression estimator
Wang, Song-Gui, Chow, Shein-Chung
The problem of estimating parameters in a linear regression model is considered. A class of adaptive generalized ridge estimator is proposed. It is shown that the proposed estimator has smaller mean...
On the measures of multicollinearity in least squares regression
Wang, Song-Gui, Tse, Siu-Keung, Chow, Shein-Chung
For a general regression model y = X[beta] + e, E(e) = 0, Cov(e) = [sigma]2V-1, some results on the relationship between two measures of multicollinearity, the eigenvalues and the condition numbers...
Estimation for parameters of interest in random effects growth curve models
Ip, Wai-Cheung, Wu, Mi-Xia, Wang, Song-Gui, Wong, Heung
In this paper, we consider the general growth curve model with multivariate random effects covariance structure and provide a new simple estimator for the parameters of interest. This estimator is...
Restricted expected multivariate least squares
Fang, Kai-Tai, Wang, Song-Gui, Von Rosen, Dietrich
A new approach of estimating parameters in multivariate models is introduced. A fitting function will be used. The idea is to estimate parameters so that the fitting function equals or will be close...
Improved estimation of the covariance matrix under Stein's loss
In this paper, the problem of estimating the covariance matrix of a multivariate normal population is considered. Some new classes of orthogonally invariant minimax estimators which include random...