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首页> 外文期刊>South African statistical journal >PREDICTION ERROR ESTIMATION OF THE SURVEY-WEIGHTED LEAST SQUARES MODEL UNDER COMPLEX SAMPLING
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PREDICTION ERROR ESTIMATION OF THE SURVEY-WEIGHTED LEAST SQUARES MODEL UNDER COMPLEX SAMPLING

机译：复杂采样下调查加权最小二乘模型的预测误差估计

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摘要

Linear modelling with the objective to predict a future response is ubiquitous in statistical analysis. Methods such as cross-validation and the bootstrap are well known for estimating the predictive performance of a model fitted to i.i.d. data. However, many large-scale surveys make use of a complex sampling design where the data are no longer i.i.d. and sampling weights are assigned to each observation to account for this. This paper shows how the cross-validation and bootstrap methods need to be adapted to evaluate the predictive performance of the survey-weighted least squares model. The investigation of the performance of the different prediction error estimation methods is evaluated through a simulation study. The Income and Expenditure Survey 2005/2006 of Statistics South Africa will form the basis of the analysis. The simulation study will also investigate whether the model's predictive performance is improved through the truncation of outlier sampling weights. For this purpose, two new thresholds, viz. the 1.5IQR and Hill, are introduced. It was found that the bootstrap estimator of prediction error achieved lower mean squared error while the K-fold cross-validation estimator achieved lower bias. Further improvement was observed using the 1.5IQR and Hill truncated sampling weights.
机译：线性建模，目的是预测未来响应在统计分析中普遍存在。诸如交叉验证和自举的方法是众所周知的，用于估计适合I.I.D的模型的预测性能。数据。然而，许多大规模调查利用复杂的采样设计，其中数据不再是i.i.d.和采样权重被分配给每个观察来解释这一点。本文展示了如何适应交叉验证和引导方法来评估调查加权最小二乘模型的预测性能。通过模拟研究评估对不同预测误差估计方法的性能的研究。 2005/2006年统计南非的收入和支出调查将成为分析的基础。仿真研究还将调查模型的预测性能是否通过截断异常量采样权重改善。为此目的，两个新的阈值，viz。 1.5iqr和山丘介绍。发现预测误差的引导估计器实现了较低的平均平方误差，而k折交叉验证估计器实现了较低的偏置。使用1.5IQR和山坡截短的采样权重观察到进一步改进。

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