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<p>In this paper, we propose a new efficient estimator for the weighted exponential family and its underlying components. These components constitute a flexible class of distributions within the standard exponential family, characterized by positive support and a generator function. For such models, maximum likelihood estimators (MLEs) are often unavailable in closed form and must be derived through numerical optimization. To address this limitation, an asymptotically efficient closed-form estimator was developed for these distributions. Monte Carlo simulations demonstrate that the proposed estimator achieves performance nearly identical to the numerically computed MLE while consistently outperforming previously proposed closed-form estimators.</p>

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Novel fast and asymptotically efficient estimation in weighted exponential family

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Hyeonwoo Kim,
  • JungJae Choi,
  • Hyoung-Moon Kim

摘要

In this paper, we propose a new efficient estimator for the weighted exponential family and its underlying components. These components constitute a flexible class of distributions within the standard exponential family, characterized by positive support and a generator function. For such models, maximum likelihood estimators (MLEs) are often unavailable in closed form and must be derived through numerical optimization. To address this limitation, an asymptotically efficient closed-form estimator was developed for these distributions. Monte Carlo simulations demonstrate that the proposed estimator achieves performance nearly identical to the numerically computed MLE while consistently outperforming previously proposed closed-form estimators.