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<p>In this paper, we propose a robust goodness-of-fit test based on the empirical characteristic function of the sample median. The test is specifically designed to address the challenges of statistical inference in small to moderate sample sizes, where traditional methods may be affected by a few extreme observations or by endpoint effects (e.g., bounded support, heavy tails). By leveraging the inherent robustness of the median and the descriptive power of the characteristic function, the proposed test exhibits stable and reliable performance across a wide range of settings. Our main contribution is the development of a goodness-of-fit procedure that combines a median-based subsampling scheme with the empirical characteristic function, resulting in a test that is both robust to outliers and effective in small-sample regimes. Although our theoretical results are derived under a two-dimensional asymptotic regime with both the number of subsamples <i>n</i> and the within-subsample size <i>N</i> increasing, the test is calibrated at fixed (<i>n</i>,&#xa0;<i>N</i>) using Monte Carlo simulation. The method is designed for scenarios with small within-subsample sizes <i>N</i> (single digits to low tens) and a small-to-moderate number of subsamples <i>n</i> (about 10–50). In simulations and applications from reliability and quality control, this regime yields accurate size and competitive power.</p>

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A robust goodness-of-fit test based on the empirical characteristic process of the median

  • 期刊论文

  • 发表日期：

    2026年7月16日

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  • Božidar V. Popović,
  • Andjela Mijanović,
  • Viktor Witkovský

摘要

In this paper, we propose a robust goodness-of-fit test based on the empirical characteristic function of the sample median. The test is specifically designed to address the challenges of statistical inference in small to moderate sample sizes, where traditional methods may be affected by a few extreme observations or by endpoint effects (e.g., bounded support, heavy tails). By leveraging the inherent robustness of the median and the descriptive power of the characteristic function, the proposed test exhibits stable and reliable performance across a wide range of settings. Our main contribution is the development of a goodness-of-fit procedure that combines a median-based subsampling scheme with the empirical characteristic function, resulting in a test that is both robust to outliers and effective in small-sample regimes. Although our theoretical results are derived under a two-dimensional asymptotic regime with both the number of subsamples n and the within-subsample size N increasing, the test is calibrated at fixed (n, N) using Monte Carlo simulation. The method is designed for scenarios with small within-subsample sizes N (single digits to low tens) and a small-to-moderate number of subsamples n (about 10–50). In simulations and applications from reliability and quality control, this regime yields accurate size and competitive power.