The method of target estimation developed by Cabrera and Fernholz to reduce bias and variance is extended to multivariate situations. For a p-dimensional statistic, conditions are given to ensure no bias and smaller variance after targeting. Some applications of multivariate targeting are given for location-scale families. The main application of multivariate targeting is presented for typical applied problems in computer vision such as ellipse estimation. For these cases, a computer-intensive procedure based on stochastic approximation is used to compute the target estimates corresponding to the least squares estimates of the ellipse parameters. In the examples presented, the data are discretized to the image resolution to make the situation more realistic in the context of computer vision. In most of the cases the bias and the mean square error of the least squares estimates are reduced after targeting. Comparisons with the bootstrap show the advantage of using targeting to obtain a more accurate reconstructed ellipse when only an arc of points is available.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Ellipse estimation
- Mean square error
- Target estimation