A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
On the estimation of variance in unstable condition adjustment models
Abstract Estimation of variance in an ordinary adjustment model is straightforward, but if the model becomes unstable or ill-conditioned its solution and the variance of the solution will be very sensitive to the errors of observations. This sensitivity can be controlled by stabilizing methods but the results will be distorted due to stabilization. In this paper, stabilizing an unstable condition model using Tikhonov regularization, the estimations of variance of unit weight and variance components are investigated. It will be theoretically proved that the estimator of variance or variance components has not the minimum variance property when the model is stabilized, but unbiased estimation of variance is possible. A simple numerical example is provided to show the performance of the theory.
On the estimation of variance in unstable condition adjustment models
Abstract Estimation of variance in an ordinary adjustment model is straightforward, but if the model becomes unstable or ill-conditioned its solution and the variance of the solution will be very sensitive to the errors of observations. This sensitivity can be controlled by stabilizing methods but the results will be distorted due to stabilization. In this paper, stabilizing an unstable condition model using Tikhonov regularization, the estimations of variance of unit weight and variance components are investigated. It will be theoretically proved that the estimator of variance or variance components has not the minimum variance property when the model is stabilized, but unbiased estimation of variance is possible. A simple numerical example is provided to show the performance of the theory.
On the estimation of variance in unstable condition adjustment models
Eshagh, M. (author)
2011
Article (Journal)
English
Adjustment, variance component estimation and testing with the affine and similarity transformations
| Online Contents | 1993
Width Adjustment: Relative Dominance in Unstable Alluvial Streams
| British Library Conference Proceedings | 1994
Variance Component Estimation in Linear Inverse Ill-posed Models
| Online Contents | 2006
Variance Component Estimation in Linear Inverse Ill-posed Models
| Online Contents | 2006