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<p>In this paper, we explore the idea of comparing two multiple linear regression (MLR) models using the multistage sequential sampling approach. In particular, we intend to compare the linear parametric functions of two MLR models with standardized predictors while fixing the upper bounds on type I and type II error probabilities. We establish that such a comparison is not possible with any fixed-sample statistical technique. Therefore, we propose an optimal three-stage sequential sampling strategy to solve this problem. We study various attractive properties of the associated stopping rule, namely <i>first-order efficiency</i>, <i>second-order efficiency</i>, and <i>asymptotic consistency</i>. We also provide brief analyses on composite hypotheses, power comparisons, and sensitivity of the proposed methodology. The practical implications and limitations of the model assumptions are also discussed. An extensive simulation analysis is performed to validate the theoretical findings, and an application based on <i>Boston housing data</i> is provided for illustration purposes.</p>

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A three-stage sequential sampling procedure for comparing linear parametric functions of two multiple linear regression models with standardized predictors: illustration using Boston housing data

  • 期刊论文

  • 发表日期：

    2026年6月18日

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  • Ashwani Rajput,
  • Neeraj Joshi

摘要

In this paper, we explore the idea of comparing two multiple linear regression (MLR) models using the multistage sequential sampling approach. In particular, we intend to compare the linear parametric functions of two MLR models with standardized predictors while fixing the upper bounds on type I and type II error probabilities. We establish that such a comparison is not possible with any fixed-sample statistical technique. Therefore, we propose an optimal three-stage sequential sampling strategy to solve this problem. We study various attractive properties of the associated stopping rule, namely first-order efficiency, second-order efficiency, and asymptotic consistency. We also provide brief analyses on composite hypotheses, power comparisons, and sensitivity of the proposed methodology. The practical implications and limitations of the model assumptions are also discussed. An extensive simulation analysis is performed to validate the theoretical findings, and an application based on Boston housing data is provided for illustration purposes.