Abstract A multivariate Birnbaum–Saunders distribution is introduced to consider a new nonparametric multivariate density estimation for nonnegative data. By construction, the estimator is the average of varying nonnegative kernel with correlation structure, whose support matches the support of the density to be estimated, unlike the classical Rosenblatt–Parzen kernel density estimator. The proposed kernel density estimator is nonnegative, boundary-bias-free and has desirable asymptotic properties. The finite sample performance of the estimator is investigated for the bivariate case.

中文翻译：

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非负数据的多元非中心 Birnbaum-Saunders 核密度估计量

摘要 引入了多元 Birnbaum-Saunders 分布以考虑非负数据的新非参数多元密度估计。通过构造，与经典的 Rosenblatt-Parzen 核密度估计器不同，估计量是具有相关结构的变化非负核的平均值，其支持与要估计的密度的支持相匹配。提出的核密度估计器是非负的、无边界偏差的并且具有理想的渐近特性。针对二元情况研究了估计器的有限样本性能。