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This study introduces new statistical estimators for skewed distributions caused by non-random sampling. These estimators are robust and efficient for accurately determining population location, even with imperfect data.

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Sample selection bias can distort statistical analyses.
  • Non-randomly sampled data often leads to skewed distributions.
  • Accurate estimation of population parameters is crucial in many fields.

Purpose of the Study:

  • To develop robust and efficient estimators for population location under semiparametric skewed distributions.
  • To address challenges posed by non-random sample selection.
  • To provide reliable statistical methods for analyzing biased data.

Main Methods:

  • Utilizing semiparametric theory for distribution modeling.
  • Developing consistent estimators robust to model mis-specification.
  • Proposing efficient estimators to minimize estimation variance.
  • Employing asymptotic analysis for theoretical validation.
  • Conducting simulation studies to assess finite sample performance.

Main Results:

  • The proposed estimators demonstrate theoretical consistency and efficiency.
  • Asymptotic analysis confirms the desirable statistical properties of the estimators.
  • Simulation results show good finite sample performance.
  • The methodology is successfully applied to real-world ambulatory expenditure data.

Conclusions:

  • The developed semiparametric skewed distribution estimators are effective for non-randomly sampled data.
  • The estimators offer robustness and efficiency, improving upon existing methods.
  • The practical application highlights the utility of the methodology in empirical research.