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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Variance estimation using memory type estimators based on EWMA statistic for time scaled surveys in stratified

Muhammad Umair Tariq1, Muhammad Nouman Qureshi2, Osama Abdulaziz Alamri3

  • 1Department of Statistics, National College of Business Administration and Economics, Lahore, Pakistan.

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|November 4, 2024
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Summary
This summary is machine-generated.

New memory-type estimators improve population variance estimation in stratified sampling by using past data. These enhanced methods offer greater accuracy for time-scaled surveys compared to traditional approaches.

Keywords:
EWMA StatisticAuxiliary informationMean squared ErrorMemory-type estimatorsStratificationTime-scaled surveys

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Traditional variance estimators in stratified sampling can be improved by incorporating historical data.
  • Existing methods may not fully leverage temporal information in surveys.

Purpose of the Study:

  • To propose novel memory-type exponential and non-exponential estimators for population variance in stratified sampling.
  • To evaluate the performance and conditions under which these new estimators outperform conventional ones.

Main Methods:

  • Development of mathematical expressions for mean square errors using Taylor and exponential expansions.
  • Derivation of conditions for the superiority of memory-type estimators.
  • Extensive simulation studies across various population parameters.
  • Application to a real-world dataset.

Main Results:

  • Memory-type estimators demonstrate superior performance over conventional estimators in stratified sampling, especially when utilizing previous sample information.
  • Mathematical conditions for improved performance were derived and validated.
  • Simulations confirmed enhanced efficiency for time-scaled surveys.
  • Real data application supported the practical utility of the proposed estimators.

Conclusions:

  • Incorporating previous sample information significantly enhances the accuracy and reliability of variance estimation in time-scaled surveys.
  • The proposed memory-type estimators offer a valuable advancement for statistical analysis in stratified sampling.
  • These findings highlight the importance of temporal data integration in survey methodology.