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Comparison of the New Estimators: The Semi-Parametric Likelihood Estimator, SPW, and the Conditional Weighted Pseudo Likelihood Estimator, WPCE

Received: 6 August 2021     Accepted: 21 August 2021     Published: 31 August 2021
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Abstract

The analysis of sample-based studies involving sampling designs for small sample size, is challenging because the sample selection probabilities (as well as the sample weights) is dependent on the response variable and covariates. The study has focused on using systems of weighted regression estimating equations, using different modified weights, to estimate the coefficients of Weighted Likelihood Estimators. Usually, the design-consistent (Weighted) estimators are obtained by solving (sample) weighted estimating equations. They are then used to construct estimates which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A. The purpose of our study is to compare derived Estimators of the weighted regression estimating equations for estimating the coefficients of Weighted Likelihood Estimators, the Semi-Parametric Weighted Likelihood Estimator, SPW and the Weighted Conditional Pseudo Likelihood Estimator, WCPE with the conventional Horvitz-Thompson Weighted Likelihood Estimator, using relative efficiency, sample bias and Standard Error for small sample size. The constructed estimates from the system of weighted regression estimating equations, using different modified weights, are actually the Weighted Likelihood Estimators. The study compared the two new estimators, the Semi-parametric weighted estimator, SPW and the Weighted Conditional Pseudo Likelihood estimator, WCPE, for both the unmodified and modified Weights, which were found to have better relative efficiency and smaller finite small sample bias than the estimates from conventional Horvitz-Thompson Weighted Estimator, for both generated and for real data. The outcome of the tests show strong similarity in performance to those obtained using the simulated data. Estimates were constructed which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A.

Published in American Journal of Theoretical and Applied Statistics (Volume 10, Issue 4)
DOI 10.11648/j.ajtas.20211004.14
Page(s) 202-207
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Semi Parametric, Imputation, Estimating Error, Small Samples, Estimators, Relative Efficiency, Sample Bias

References
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[22] Samuel J. Kamun, Richard O. Simwa and Stanley Sewe. On Derivation of the Semi-Parametric Weighted Likelihood Estimator, SPW, and the Weighted Conditional Pseudo Likelihood Estimator, WPCE, Far East Journal of Theoretical Statistics © 2021 Pushpa Publishing House, Prayagraj, India, http://www.pphmj.com, http://dx.doi.org/10.17654/
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    Samuel Joel Kamun, Richard Simwa, Stanley Sewe. (2021). Comparison of the New Estimators: The Semi-Parametric Likelihood Estimator, SPW, and the Conditional Weighted Pseudo Likelihood Estimator, WPCE. American Journal of Theoretical and Applied Statistics, 10(4), 202-207. https://doi.org/10.11648/j.ajtas.20211004.14

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    Samuel Joel Kamun; Richard Simwa; Stanley Sewe. Comparison of the New Estimators: The Semi-Parametric Likelihood Estimator, SPW, and the Conditional Weighted Pseudo Likelihood Estimator, WPCE. Am. J. Theor. Appl. Stat. 2021, 10(4), 202-207. doi: 10.11648/j.ajtas.20211004.14

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    AMA Style

    Samuel Joel Kamun, Richard Simwa, Stanley Sewe. Comparison of the New Estimators: The Semi-Parametric Likelihood Estimator, SPW, and the Conditional Weighted Pseudo Likelihood Estimator, WPCE. Am J Theor Appl Stat. 2021;10(4):202-207. doi: 10.11648/j.ajtas.20211004.14

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  • @article{10.11648/j.ajtas.20211004.14,
      author = {Samuel Joel Kamun and Richard Simwa and Stanley Sewe},
      title = {Comparison of the New Estimators: The Semi-Parametric Likelihood Estimator, SPW, and the Conditional Weighted Pseudo Likelihood Estimator, WPCE},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {10},
      number = {4},
      pages = {202-207},
      doi = {10.11648/j.ajtas.20211004.14},
      url = {https://doi.org/10.11648/j.ajtas.20211004.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211004.14},
      abstract = {The analysis of sample-based studies involving sampling designs for small sample size, is challenging because the sample selection probabilities (as well as the sample weights) is dependent on the response variable and covariates. The study has focused on using systems of weighted regression estimating equations, using different modified weights, to estimate the coefficients of Weighted Likelihood Estimators. Usually, the design-consistent (Weighted) estimators are obtained by solving (sample) weighted estimating equations. They are then used to construct estimates which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A. The purpose of our study is to compare derived Estimators of the weighted regression estimating equations for estimating the coefficients of Weighted Likelihood Estimators, the Semi-Parametric Weighted Likelihood Estimator, SPW and the Weighted Conditional Pseudo Likelihood Estimator, WCPE with the conventional Horvitz-Thompson Weighted Likelihood Estimator, using relative efficiency, sample bias and Standard Error for small sample size. The constructed estimates from the system of weighted regression estimating equations, using different modified weights, are actually the Weighted Likelihood Estimators. The study compared the two new estimators, the Semi-parametric weighted estimator, SPW and the Weighted Conditional Pseudo Likelihood estimator, WCPE, for both the unmodified and modified Weights, which were found to have better relative efficiency and smaller finite small sample bias than the estimates from conventional Horvitz-Thompson Weighted Estimator, for both generated and for real data. The outcome of the tests show strong similarity in performance to those obtained using the simulated data. Estimates were constructed which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Comparison of the New Estimators: The Semi-Parametric Likelihood Estimator, SPW, and the Conditional Weighted Pseudo Likelihood Estimator, WPCE
    AU  - Samuel Joel Kamun
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    AB  - The analysis of sample-based studies involving sampling designs for small sample size, is challenging because the sample selection probabilities (as well as the sample weights) is dependent on the response variable and covariates. The study has focused on using systems of weighted regression estimating equations, using different modified weights, to estimate the coefficients of Weighted Likelihood Estimators. Usually, the design-consistent (Weighted) estimators are obtained by solving (sample) weighted estimating equations. They are then used to construct estimates which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A. The purpose of our study is to compare derived Estimators of the weighted regression estimating equations for estimating the coefficients of Weighted Likelihood Estimators, the Semi-Parametric Weighted Likelihood Estimator, SPW and the Weighted Conditional Pseudo Likelihood Estimator, WCPE with the conventional Horvitz-Thompson Weighted Likelihood Estimator, using relative efficiency, sample bias and Standard Error for small sample size. The constructed estimates from the system of weighted regression estimating equations, using different modified weights, are actually the Weighted Likelihood Estimators. The study compared the two new estimators, the Semi-parametric weighted estimator, SPW and the Weighted Conditional Pseudo Likelihood estimator, WCPE, for both the unmodified and modified Weights, which were found to have better relative efficiency and smaller finite small sample bias than the estimates from conventional Horvitz-Thompson Weighted Estimator, for both generated and for real data. The outcome of the tests show strong similarity in performance to those obtained using the simulated data. Estimates were constructed which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A.
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Author Information
  • Department of Mathematics and Computing Studies, Faculty of Science, Catholic University of Eastern Africa, Nairobi, Kenya

  • Department of Mathematics, Faculty of Science, University of Nairobi, Nairobi, Kenya

  • Department of Mathematics and Computing Studies, Faculty of Science, Catholic University of Eastern Africa, Nairobi, Kenya

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