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<p>We consider the problem of nonparametric classification and bandwidth estimation when the class variables (labels) may be missing but not necessarily at random, also referred to as missing <i>nonignorably</i>. This setup is acknowledged to be far more challenging than the usual missing at random setup. The proposed approach can be viewed as a two-step procedure: the first step involves the construction of a family of kernel-based classifiers where the members of the family are indexed by the kernel bandwidth <i>h</i> as well as the nonignorability parameter of the missing probability mechanism. In the second step, a search is performed to find the member of a cover of this family that has the smallest empirical misclassification error. To study the performance of our classifiers, we establish exponential performance bounds on the deviations of their errors from that of the theoretically optimal classifier. These bounds are used to establish convergence properties of our classifiers. Our numerical studies further confirm the theoretical findings of this paper.</p>

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On nonparametric classification and bandwidth selection with nonignorable missing labels

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Majid Mojirsheibani,
  • Blake Tinoco

摘要

We consider the problem of nonparametric classification and bandwidth estimation when the class variables (labels) may be missing but not necessarily at random, also referred to as missing nonignorably. This setup is acknowledged to be far more challenging than the usual missing at random setup. The proposed approach can be viewed as a two-step procedure: the first step involves the construction of a family of kernel-based classifiers where the members of the family are indexed by the kernel bandwidth h as well as the nonignorability parameter of the missing probability mechanism. In the second step, a search is performed to find the member of a cover of this family that has the smallest empirical misclassification error. To study the performance of our classifiers, we establish exponential performance bounds on the deviations of their errors from that of the theoretically optimal classifier. These bounds are used to establish convergence properties of our classifiers. Our numerical studies further confirm the theoretical findings of this paper.