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Updated: Jun 24, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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On bootstrap based variance estimation under fine stratification.

Alexis Habineza1,2, Romanus Odhiambo Otieno3,4, George Otieno Orwa3

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Summary

This study introduces a novel bootstrap-based variance estimator for fine stratification in surveys. It effectively addresses the overestimation issues found in traditional collapsed stratum methods, improving estimate accuracy.

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Area of Science:

  • Survey Methodology
  • Statistical Inference
  • Sampling Theory

Background:

  • Sample surveys aim to provide accurate point estimates and quantify uncertainty through variance estimation.
  • Fine stratification divides populations into small strata, ensuring subgroup representation but complicating variance estimation with small sample sizes.
  • Traditional collapsed stratum techniques for variance estimation in fine stratification are known to be biased, leading to overestimation.

Purpose of the Study:

  • To propose a new bootstrap-based variance estimator for total population under fine stratification.
  • To address the limitations of existing methods, specifically the bias and overestimation associated with the collapsed stratum technique.
  • To investigate the properties and performance of the proposed estimator.

Main Methods:

  • Development of a novel bootstrap-based variance estimator tailored for fine stratification designs.
  • Theoretical investigation into the properties of the proposed estimator.
  • Empirical evaluation through a simulation study and a real-world application using mental health organizations survey data.

Main Results:

  • The proposed bootstrap-based variance estimator effectively overcomes the drawbacks of the collapsed stratum technique.
  • Simulation studies and practical application demonstrated the good performance of the new estimator.
  • The new method provides more accurate and stable variance estimates in fine stratification scenarios.

Conclusions:

  • The bootstrap-based variance estimator offers a superior alternative to traditional methods in fine stratification.
  • Accurate variance estimation is crucial for reliable survey results, especially in complex designs.
  • The proposed method enhances the precision and reliability of survey estimates in situations with numerous small strata.