Using Nonlinear Models to Enhance Prediction Performance with Incomplete Data
Using Nonlinear Models to Enhance Prediction Performance with Incomplete Data
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DOI：
10.5220/0005157201410148
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发表时间：
2015-01
期刊：
影响因子：
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通讯作者：
Faraj A. A. Bashir-Faraj-A.-A.-Bashir-3106601;Hua-Liang Wei
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文献类型：
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作者：
Faraj A. A. Bashir-Faraj-A.-A.-Bashir-3106601;Hua-Liang Wei
近年来缺失数据分析的方法学研究主要集中在利用最大似然和多重插值等现代统计方法估计模型参数。这些方法比传统的方法（例如列表删除和平均imputation方法）更好。这些现代技术可以在许多特定的应用情况下导致无偏参数估计。然而，这些方法在某些情况下并不能很好地工作，特别是对于具有高度非线性行为的非线性系统。本文阐述了缺失数据下的线性参数估计，概述了缺失数据下的有偏和无偏线性参数估计，并给出了期望最大化算法和高斯-牛顿方法的描述。特别地，本文提出了一种用于数据缺失情况下非线性参数估计的高斯-牛顿迭代方法。由于高斯-牛顿法需要的初值在数据缺失的情况下难以获得，因此使用EM算法来估计这些初值。此外，我们还提供了两个分析示例来说明所提出方法的性能。
A great deal of recent methodological research on missing data analysis has focused on model parameter estimation using modern statistical methods such as maximum likelihood and multiple imputation. These approaches are better than traditional methods (for example listwise deletion and mean imputation methods). These modern techniques can lead to unbiased parametric estimation in many particular application cases. However, these methods do not work well in some cases especially for nonlinear systems that have highly nonlinear behaviour. This paper explains the linear parametric estimation in existence of missing data, which includes an overview of biased and unbiased linear parametric estimation with missing data, and provides accessible descriptions of expectation maximization (EM) algorithm and Gauss-Newton method. In particular, this paper proposes a Gauss-Newton iteration method for nonlinear parametric estimation in case of missing data. Since Gauss-Newton method needs initial values that are hard to obtain in the presence of missing data, the EM algorithm is thus used to estimate these initial values. In addition, we present two analysis examples to illustrate the performance of the proposed methods.