Geodesic
On applying Monte Carlo methods to analysis of nonlinear regression models
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 4, pp. 425-434

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This paper presents a criterium, called the coefficients stability for inaccuracy in determining the coefficients of nonlinear regression models describing inexact data. A`method for the coefficients stability estimation is also described. The proposed criterium is illustrated by a computational experiment with the data obtained by measurements of a refractive index dependence on the wavelength in 400–1000 nm band for a transparent polymer. The convergence of the proposed criterium to the known analytical solution for the case of linear regression is also studied. 
@article{SJVM_2015_18_4_a6,
     author = {G. I. Rudoy},
     title = {On applying {Monte} {Carlo} methods to analysis of nonlinear regression models},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {425--434},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2015_18_4_a6/}
}
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G. I. Rudoy. On applying Monte Carlo methods to analysis of nonlinear regression models. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 4, pp. 425-434. http://geodesic.mathdoc.fr/item/SJVM_2015_18_4_a6/