A least squares-type density estimator using a polynomial function
A least squares-type density estimator using a polynomial function
复制标题
使用多项式函数的最小二乘型密度估计器
DOI：
10.1016/j.csda.2019.106882
复制
发表时间：
2020
影响因子：
1.8
通讯作者：
H.-T.
中科院分区：
文献类型：
--
作者：
Im;J.;Morikawa;K.;and Ha;H.-T.
使用正交级数展开的高阶密度近似和估计方法在统计文献及其各个应用领域中得到了广泛的讨论。通过最小化级数分布展开的加权平方差和一个基准分布估计器，提出了级数展开的最小二乘估计。由于最小二乘型估计量具有类似于经典矩匹配技术的显式表达式，因此在一定的正则性条件下，它的渐近性质很容易得到。此外，我们还利用二次规划解决了级数展开的非负性问题。各种模拟和真实数据集的数值算例表明了该估计器的优越性。
Higher-order density approximation and estimation methods using orthogonal series expansion have been extensively discussed in statistical literature and its various fields of application. This study proposes least squares-type estimation for series expansion via minimizing the weighted square difference of series distribution expansion and a benchmarking distribution estimator. As the least squares-type estimator has an explicit expression, similar to the classical moment-matching technique, its asymptotic properties are easily obtained under certain regularity conditions. In addition, we resolve the non-negativity issue of the series expansion using quadratic programming. Numerical examples with various simulated and real datasets demonstrate the superiority of the proposed estimator.