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<p>Using replicated measurements improves accuracy and stability by reducing random error. This study analyzes covariates with replicated observations in a linear measurement error model with heteroscedasticity. We extend the adjusted least squares (ALS) and derive asymptotic covariance matrices using both sandwich (SW) and model-based (MB) approaches grounded in unbiased estimating equations. Through simulation studies, we evaluate the performance of the estimators and confidence intervals in terms of bias, mean squared error, coverage probability, and rejection rate. We also propose a novel procedure for anomaly detection. A real PM<sub>2.5</sub> dataset illustrates the methodology: observations from distributed sensors and government monitoring stations are modeled as having a linear relationship. The results show that several sensors exhibit anomalous measurements and require calibration under the proposed method.</p>

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Anomaly Detection in Linear Regression Model with Heteroscedastic Errors Using Replicated Measurements

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Jia-Ren Tsai,
  • Ting-I Lei,
  • Sheng-Wei Hsiao

摘要

Using replicated measurements improves accuracy and stability by reducing random error. This study analyzes covariates with replicated observations in a linear measurement error model with heteroscedasticity. We extend the adjusted least squares (ALS) and derive asymptotic covariance matrices using both sandwich (SW) and model-based (MB) approaches grounded in unbiased estimating equations. Through simulation studies, we evaluate the performance of the estimators and confidence intervals in terms of bias, mean squared error, coverage probability, and rejection rate. We also propose a novel procedure for anomaly detection. A real PM2.5 dataset illustrates the methodology: observations from distributed sensors and government monitoring stations are modeled as having a linear relationship. The results show that several sensors exhibit anomalous measurements and require calibration under the proposed method.