On Computing Objective Function and Gradient in the Context of Least Squares Fitting a Dynamic Errors-In-Variables Model
Copyright policy )On Computing Objective Function and Gradient in the Context of Least Squares Fitting a Dynamic Errors-In-Variables Model
The estimation of the parameters in a special linear prediction model is discussed. All variables are observed subject to errors. For this situation we introduce an estimation method which results in a nonlinear optimization problem to be solved. Basically, this paper contains a new method for the computation of the corresponding objective function and its gradient. The first section is dedicated to the description of the estimation problem and the introduction of the estimation method. In the next section, expressions for objective function and gradient are derived. Depending on the choice of the iterative optimization algorithm, one or more evaluations of objective function and gradient are required per iteration. The main contribution of the paper is the algebraic scheme for computing objective function and gradient values. This scheme is based on the QR decomposition of a matrix with special structure. In the final section, among others, comparisons with other methods are given.
- Wageningen University & Research Netherlands
Numerical optimization and variational techniques, Toeplitz structure, least squares method, Point estimation, iterative optimization algorithm, Probabilistic methods, stochastic differential equations, nonlinear optimization, Orthogonalization in numerical linear algebra, gradient, linear prediction model, QR decomposition, Linear inference, regression, objective function, Life Science, errors-in-variables, Applications of statistics to economics
Numerical optimization and variational techniques, Toeplitz structure, least squares method, Point estimation, iterative optimization algorithm, Probabilistic methods, stochastic differential equations, nonlinear optimization, Orthogonalization in numerical linear algebra, gradient, linear prediction model, QR decomposition, Linear inference, regression, objective function, Life Science, errors-in-variables, Applications of statistics to economics
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