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首页> 外文期刊>Journal of applied and industrial mathematics >Estimating Parameters of Polynomial Models with Errors in Variables and No Additional Information
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Estimating Parameters of Polynomial Models with Errors in Variables and No Additional Information

机译：无变量且无附加信息的多项式模型的参数估计

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摘要

The problem of estimating a polynomial model with a classical error in the input factor is under consideration in the functional case. The nonparametric method recently introduced for estimating structural dependences does not use any additional information, but it is very effortconsuming computationally and needs samples of large size.We propose some easier methods. The first approach is based on a preliminary estimation of the Berkson error variance under assumption of its normal distribution by the maximum likelihood method for a piecewise linearmodel. This estimate of variance is used for recovering the parameters of a polynomial by the methods of general and adjusted least squares. In case the error variance deviates from normal distribution, an adaptive method is developed that is based on the generalized lambda distribution. These approaches were applied for solving the problem of knowledge level evaluation.
机译：在功能情况下，正在考虑用输入因子的经典误差来估计多项式模型的问题。最近引入的用于估计结构相关性的非参数方法不使用任何其他信息，但是它在计算上非常费力，并且需要大量样本。我们提出了一些更简单的方法。第一种方法是基于分段线性模型的最大似然法，在伯克森误差方差为正态分布的前提下，对伯克森误差方差进行初步估计。该方差估计用于通过通用和调整最小二乘法来恢复多项式的参数。在误差方差偏离正态分布的情况下，开发了一种基于广义λ分布的自适应方法。这些方法被用于解决知识水平评估的问题。

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