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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Estimation in additive models and ANOVA-like applications.

Patrícia Antunes1, Sandra S Ferreira1,2, Dário Ferreira1,2

  • 1Center of Mathematics, University of Beira Interior, Covilhã, Portugal.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study estimates cumulants using least-squares estimators and a cumulant generating function property. The method shows good performance and flexibility when applied to real data for statistical analysis.

Keywords:
62J1062K99ANOVAcumulantslinear modelsmoments

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Area of Science:

  • Statistics
  • Statistical Modeling

Background:

  • Cumulants are essential statistical measures for characterizing probability distributions.
  • Estimating higher-order cumulants can be challenging, particularly in complex models.

Purpose of the Study:

  • To develop and evaluate a method for estimating the first four order cumulants.
  • To obtain empirical best linear unbiased predictors for additive models.
  • To provide unbiased estimators for fourth-order cumulants using specific model pairings.

Main Methods:

  • Utilizing a known property of the cumulant generating function.
  • Applying least-squares estimators for cumulant estimation.
  • Employing pairs of independent and identically distributed models for unbiased fourth-order cumulant estimation.

Main Results:

  • Least-squares estimators demonstrated good behavior in real data application.
  • The proposed approach offers significant flexibility in statistical analysis.
  • Empirical best linear unbiased predictors were successfully obtained for additive models.

Conclusions:

  • The least-squares estimation method is effective for cumulant estimation.
  • The approach is flexible and applicable to real-world statistical problems.
  • The use of paired models provides a robust way to estimate fourth-order cumulants.