Geodesic
Estimating polynomial models with errors in variables without additional information
Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 3, pp. 15-27

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We consider the problem of estimating a polynomial model with classical error in the input factor in the functional case. The nonparametric method of estimation of structural dependencies does not use additional information but is extremely hard computationally and requires a large sample size. That is why we propose a number of easier approaches. The first approach is based on the preliminary estimation of the Berkson error variance under the assumption of its normality for a piecewise-linear model. The so-obtained estimate is used to calculating the parameters of the polynomial by the methods of general and adjusted least squares. In the case when the error distribution deviates from the normal distribution, we develop a second method, the adaptive estimation method, based on the universal lambda-distribution. The proposed approaches were developed for solving the problem of analyzing the level of knowledge.
Keywords: model with errors in both variables, method of generalized least squares, method of adjusted least squares, maximum likelihood method, adaptive method, generalized distribution. 
@article{SJIM_2016_19_3_a1,
     author = {V. I. Denisov and A. Yu. Timofeeva and E. A. Khailenko},
     title = {Estimating polynomial models with errors in variables without additional information},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {15--27},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2016_19_3_a1/}
}
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V. I. Denisov; A. Yu. Timofeeva; E. A. Khailenko. Estimating polynomial models with errors in variables without additional information. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 3, pp. 15-27. http://geodesic.mathdoc.fr/item/SJIM_2016_19_3_a1/