Skewing methods for two-parameter locally parametric density estimation
Skewing methods for two-parameter locally parametric density estimation
复制标题
二参数局部参数密度估计的偏斜方法
作者：
Ming;E. Choi;Jianqing Fan;P. Hall
一个“偏斜”的方法，有效地降低了当地的参数估计偏差的顺序，并在同一时间保持积极的性质。该技术涉及到首先计算通常的局部参数近似在附近的一个点x'，这是一个短距离的地方x，我们希望估计的密度，然后评估这个近似在x。通过比较，通常的局部参数方法采用x '= x。在我们的构造中，x '-x以一种非常简单的方式依赖于带宽和内核，而根本不依赖于未知密度。以这种简单的形式使用偏斜将偏差的阶数从带宽的平方降低到带宽的立方;并且取以这种方式计算的两个估计量的平均值进一步将偏差降低到带宽的四次方。另一方面，方差最多只增加一个适度的常数因子。
A `skewing' method is shown to effectively reduce the order of bias of locally parametric estimators, and at the same time retain positivity properties. The technique involves first calculating the usual locally parametric approximation in the neighbourhood of a point x' that is a short distance from the place x where the we wish to estimate the density, and then evaluating this approximation at x. By way of comparison, the usual locally parametric approach takes x'=x. In our construction, x'-x depends in a very simple way on the bandwidth and the kernel, and not at all on the unknown density. Using skewing in this simple form reduces the order of bias from the square to the cube of bandwidth; and taking the average of two estimators computed in this way further reduces bias, to the fourth power of bandwidth. On the other hand, variance increases only by at most a moderate constant factor.
影响因子：
4.5
作者：
N. Hjort;M. C. Jones
通讯作者：
N. Hjort;M. C. Jones