Second-order approximation of the entropy in nonlinear least-squares estimation
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Sensitivity analysis of -estimators of non-linear regression models
Asunción Rubio, Francisco Quintana, Jan Ámos Víšek (1994)
Commentationes Mathematicae Universitatis Carolinae
An asymptotic formula for the difference of the -estimates of the regression coefficients of the non-linear model for all observations and for observations is presented under conditions covering the twice absolutely continuous -functions. Then the implications for the -estimation of the regression model are discussed.
Separable least squares, variable projection, and the Gauss-Newton algorithm.
Osborne, M.R. (2007)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Sequential estimation method for the minimum of a quadratic regression function
M. Męczarski (1987)
Applicationes Mathematicae
Some limit properties of an approximate least squares estimator in a nonlinear regression model with correlated nonzero mean errors.
Kalická, J. (1996)
Acta Mathematica Universitatis Comenianae. New Series
Some remarks on experimental design
Marie Hušková, Jan Ámos Víšek, Dana Vorlíčková (1986)
Aplikace matematiky
The paper deals with the experimental design which is optimal in the following sense: it satisfies the cost requirements simultaneously with a satisfactory precision of estimates. The underlying regression model is quadratic. The estimates of unknown parameters of the model are explicitly derived.
Strong consistency of regression function estimates
Zhang Shuang Lin (1995)
Kybernetika
Suitability of linearization of nonlinear problems not only in biology and medicine
Jana Vrbková (2009)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Biology and medicine are not the only fields that present problems unsolvable through a linear models approach. One way to overcome this obstacle is to use nonlinear methods, even though these are not as thoroughly explored. Another possibility is to linearize and transform the originally nonlinear task to make it accessible to linear methods. In this aricle I investigate an easy and quick criterion to verify suitability of linearization of nonlinear problems via Taylor series expansion so that...
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