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Least Squares Estimation Principle and its Geometrical Interpretation
pdf contains 14 pages
Properties of the total least squares estimation
Abstract:Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given
Least Squares estimation of two ordered monotone regression curves
In this paper, we consider the problem of finding the Least Squares
estimators of two isotonic regression curves and under
the additional constraint that they are ordered; e.g., . Given two sets of data points and observed at (the same) design points, the estimates of the true
curves are obtained by minimizing the weighted Least Squares criterion
over the class of pairs of vectors such that , , and
. The characterization of the estimators is
established. To compute these estimators, we use an iterative projected
subgradient algorithm, where the projection is performed with a "generalized"
pool-adjacent-violaters algorithm (PAVA), a byproduct of this work. Then, we
apply the estimation method to real data from mechanical engineering.Comment: 23 pages, 2 figures. Second revised version according to reviewer
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A survey of the state of the art and focused research in range systems, task 2
Contract generated publications are compiled which describe the research activities for the reporting period. Study topics include: equivalent configurations of systolic arrays; least squares estimation algorithms with systolic array architectures; modeling and equilization of nonlinear bandlimited satellite channels; and least squares estimation and Kalman filtering by systolic arrays
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