New methods for bias correction at endpoints and boundaries
New methods for bias correction at endpoints and boundaries
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DOI：
10.1214/aos/1035844983
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发表时间：
2002-10
影响因子：
4.5
通讯作者：
P. Hall;B. Park
中科院分区：
文献类型：
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作者：
P. Hall;B. Park
我们提出了两个新的，基于修正的方法估计和校正偏差时，估计边缘的分布。第一个使用经验翻译适用于内核的参数，以消除主要影响的不对称性是固有的，当构建估计在边界。将翻译放在内核内部与传统方法形成鲜明对比，例如使用高阶内核，这与折刀相关，实际上，将翻译应用于内核外部。我们的方法具有产生偏差估计的优势，同时享有较高的精度，保证尊重偏差的符号。我们的第二种方法是一种新的bootstrap技术。它涉及将初始边界估计值向数据集主体平移，从位于相应平移下方的数据中构建重复的边界估计值，并采用所得经验偏差近似值的平均值来估计原始估计值的偏差。这两种方法中的第一种最适合于单变量情况，并在那里进行了研究;第二种方法可用于多变量分布边界的偏差校正估计，并在双变量情况下进行了探索。
We suggest two new, translation-based methods for estimating and correcting for bias when estimating the edge of a distribution. The first uses an empirical translation applied to the argument of the kernel, in order to remove the main effects of the asymmetries that are inherent when constructing estimators at boundaries. Placing the translation inside the kernel is in marked contrast to traditional approaches, such as the use of high-order kernels, which are related to the jackknife and, in effect, apply the translation outside the kernel. Our approach has the advantage of producing bias estimators that, while enjoying a high order of accuracy, are guaranteed to respect the sign of bias. Our second method is a new bootstrap technique. It involves translating an initial boundary estimate toward the body of the dataset, constructing repeated boundary estimates from data that lie below the respective translations, and employing averages of the resulting empirical bias approximations to estimate the bias of the original estimator. The first of the two methods is most appropriate in univariate cases, and is studied there; the second approach may be used to bias-correct estimates of boundaries of multivariate distributions, and is explored in the bivariate case.