Translated Title
Two-stage Estimate of the Circle Parameters
Translated Abstract
The problem of fitting a circle to a set of observations occurs often in many engineering and technology. A two-stage estimate (TSE) of a circle and radius is proposed by using linear model with heteroscedastic variances. Based on special construction of the design matrix, some interesting relations of variance matrices of the least squares estimate (LSE), the best linear unbiased estimate (BLUE) and the TSE are established, and some important properties of the TSE are obtained. In particular, a sufficient condition for the TSE to be superior over the LSE is given. In terms of Kantorovich inequality, a lower bound of a relative efficiency of the TSE with respect to the BLUE is also obtained. This bound shows, even if the sample size is not large, the TSE also have higher relative efficiency.Finally, an optimality of the LSE is given when the observations are equally spaced around the circle.
Translated Keyword
variance component
relative efficiency
Two-stage estimate
least squares estimate
Access Number
WF:perioarticalgcsxxb200405006
Corresponding authors email
