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A Conditional Least Squares Approach to Bilinear Time Series Estimation [PDF]

Journal of Time Series Analysis, 1995
Abstract.In this paper a conditional least squares (CLS) procedure for estimating bilinear time series models is introduced. This method is applied to a special superdiagonal bilinear model which includes the classical linear autoregressive moving‐average model as a particular case and it is proven that the limiting distribution of the CLS estimates is
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Least squares computations and the condition of the matrix

Communications in Statistics - Simulation and Computation, 1981
In the days of Von Neumann and Goldstine (1947), when matrix inversion was in vogue, the condition of the regression matrix in least squares problems held great relevance to both the sensitivity of its inverse to relatively small perturbations in its coefficients, and also to the number of decimal digit accuracy that could be obtained in the solution ...
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Total least-squares adjustment of condition equations

Studia Geophysica et Geodaetica, 2011
The usual least-squares adjustment within an Errors-in-Variables (EIV) model is often described as Total Least-Squares Solution (TLSS), just as the usual least-squares adjustment within a Random Effects Model (REM) has become popular under the name of Least-Squares Collocation (without trend). In comparison to the standard Gauss-Markov Model (GMM), the
Burkhard Schaffrin, Andreas Wieser
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Well-Conditioned Recursive Least-Squared Estimation Algorithms

IFAC Proceedings Volumes, 1992
This paper explains the inadequacies due to ill-conditioning of classical recursive least squares signal estimation algorithms based on Taylor series expansions, then shows how the algorithms may be restructured using orthogonal expansions, at little cost in extra complexity, to provide well-conditioned versions suitable for implementation in a variety
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On Variances of Conditional Linear Least‐Squares Search Parameter Estimates

American Journal of Agricultural Economics, 1981
Among the class of models that are nonlinear in the parameters, some lend themselves to a simple estimation method requiring repeated application of linear least squares. However, there is confusion over methods for computing standard errors of such estimates. In this paper we define a simple method for estimating parameters of certain nonlinear models
Edmund A. Estes, Leroy L. Blakeslee, Ron C. Mittelhammer   +2 more
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A Procedure for Nonlinear Least Squares Refinement in Adverse Practical Conditions

Journal of the ACM, 1966
An iterative method is described for computing optimum values of a set of parameters for the best agreement in a least squares between a given set of (experimental) values and corresponding calculated (theoretical) values where these may be dependent non-linearly on the parameters. The method is for use when (a) the amount of work in the calculation of
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The non-linear least-squares of condition equations

Bulletin géodésique, 1973
In this paper the author constructs general algorithms for the non-linear least squares of condition equations and shows the procedure of their application for the settlement of the problem of unfavorable condition equations in the adjustment of a quadrilateral.
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Least squares regression under weak moment conditions

Journal of Computational and Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Condition-Number Barrier in Sparse Least Squares

In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm. We establish their conjectured lower bound for least-squares objectives, conditional on the randomized exact-volume Small-Set Expansion Hypothesis in the weighted ...
Lin, Honghao, Mirrokni, Vahab, Woodruff, David P.   +2 more
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A Comparison of Condition Numbers for the Full Rank Least Squares Problem

2005
Condition numbers of the full rank least squares (LS) problem minx||Ax−b||2 are considered theoretically and their computational implementation is compared. These condition numbers range from a simple normwise measure that may overestimate by several orders of magnitude the true numerical condition of the LS problem, to refined componentwise and ...
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