ABSTRACT In this paper, we address the crucial necessity of understanding the behavior of the Greenwood statistic when dealing with data corrupted by multiplicative measurement errors. The unobservable variable is subject to a multiplicative distortion influenced by an unknown smoothing function dependent on a confounding variable. We introduce the conditional mean calibrated Greenwood statistic and its variants, including the coefficient of variation, to adapt to this complex situation. The asymptotic results we present showcase their effectiveness even when such distortions are present. Moreover, for general distributions of the unobserved variable, we extend the methodology by proposing calibrated‐modified Greenwood statistics and the coefficient of variation. These methods are demonstrated to be asymptotically efficient under various assumptions about the distortion function. Furthermore, we conduct Monte Carlo simulation experiments to assess the performance of the proposed estimators and test statistics, during which we compare our proposed test statistics with existing ones. For illustrative purposes, these methods are then applied to analyze a real‐world d
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