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<p>This study suggests a generalized class of estimator for population variance using auxiliary information under the Extended Exponentially Weighted Moving Average (EEWMA) scheme. The EEWMA estimator utilizes dual smoothing parameters or weighting constants to control the weighting structure of current and past sample data. Unlike EWMA, which gives a fixed memory weight, EEWMA dynamically balances short-term changes and long-term trends, making it more flexible to sudden shifts and temporal variations commonly found in environmental time-series data. Properties such as bias and Mean Squared Error (MSE), are derived up to the first order of approximation. An empirical study is carried out with a real-data application using Air Quality Index (AQI) data for Kolkata, 2024. Because of its severe peaks, seasonal dependence, and irregular oscillations caused by variations in pollutant concentrations, AQI is a perfect testbed for memory-type variance estimation techniques.</p>

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Application to Air Quality Index Data: Extended EWMA-Based Variance Estimator

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Prayas Sharma,
  • Mamta Kumari

摘要

This study suggests a generalized class of estimator for population variance using auxiliary information under the Extended Exponentially Weighted Moving Average (EEWMA) scheme. The EEWMA estimator utilizes dual smoothing parameters or weighting constants to control the weighting structure of current and past sample data. Unlike EWMA, which gives a fixed memory weight, EEWMA dynamically balances short-term changes and long-term trends, making it more flexible to sudden shifts and temporal variations commonly found in environmental time-series data. Properties such as bias and Mean Squared Error (MSE), are derived up to the first order of approximation. An empirical study is carried out with a real-data application using Air Quality Index (AQI) data for Kolkata, 2024. Because of its severe peaks, seasonal dependence, and irregular oscillations caused by variations in pollutant concentrations, AQI is a perfect testbed for memory-type variance estimation techniques.