On histogram-based regression and classification with incomplete data
On histogram-based regression and classification with incomplete data
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DOI：
10.1007/s00184-020-00794-y
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发表时间：
2020-08-19
期刊：
影响因子：
0.7
通讯作者：
Mojirsheibani，Majid
中科院分区：
文献类型：
--
作者：
Han，Eric;Mojirsheibani，Majid
本文研究了协变量向量可能不完全的非参数回归问题。建议的估计，这是基于直方图的方法，是完全非参数和简单的实现。不完整协变量的存在通过逆加权方法处理，其中权重是具有不完整协变量向量的条件概率的估计值。我们还推导出各种指数界的估计，这可以用来建立强一致性结果相应的，密切相关的，问题的非参数分类缺失协变量的理论。作为我们研究结果的主要焦点和应用，我们考虑了不完全协变量存在下的模式识别和统计分类问题，并提出了渐近最优的直方图分类器。
We consider the problem of nonparametric regression with possibly incomplete covariate vectors. The proposed estimators, which are based on histogram methods, are fully nonparametric and straightforward to implement. The presence of incomplete covariates is handled by an inverse weighting method, where the weights are estimates of the conditional probabilities of having incomplete covariate vectors. We also derive various exponential bounds on thenorms of our estimators, which can be used to establish strong consistency results for the corresponding, closely related, problem of nonparametric classification with missing covariates. As the main focus and application of our results, we consider the problem of pattern recognition and statistical classification in the presence of incomplete covariates and propose histogram classifiers that are asymptotically optimal.