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Estimating statistical properties from limited data is challenging. This study introduces a novel theoretical-computational framework for accurate statistical quantity estimation in temporal processes, even with sparse data.

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Area of Science:

  • Statistical analysis
  • Time series analysis
  • Computational modeling

Background:

  • Estimating statistical properties from empirical data is crucial across various scientific and economic fields.
  • Challenges arise from short time series or rare events, hindering accurate direct data estimation.
  • Mean first passage times and waiting times in intermittent signals are examples of such properties.

Purpose of the Study:

  • To develop a systematic and rational theoretical-computational framework for statistical quantity estimation.
  • To address limitations of direct data analysis for temporal continuous processes.
  • To enable reliable estimation even with incomplete or sparse empirical data.

Main Methods:

  • Development of a novel theoretical-computational framework.
  • Application of the framework to analyze temporal continuous processes.
  • Validation using real-world datasets from diverse fields.

Main Results:

  • The proposed framework enables systematic and rational estimation of statistical quantities.
  • Demonstrated effectiveness in scenarios with limited or rare observational data.
  • Successful application across diverse real-world datasets, including marine biology and paleoclimatology.

Conclusions:

  • The theoretical-computational framework offers a robust solution for statistical property estimation.
  • This approach enhances the reliability of analyses for temporal processes with data limitations.
  • The framework has broad applicability in physical, technological, social, and economic domains.