A New Nonparametric Estimator of the Center of a Symmetric Distribution
对称分布中心的一种新非参数估计量
Let $F_n(x)$ be the empirical distribution function based on a random sample of size $n$ from a continuous symmetric distribution with center $\theta$. As a nonparametric estimator of $\theta$, we propose $a^\ast$ where $a^\ast$ is chosen so as to minimize the function $h$ where $h(a) = \max_x |F_n(x) + F_n((2a - x)^-) - 1|$. In this paper we present an algorithm for constructing the interval of all $a$ which minimize $h$. We show that if $a^\ast$ is chosen as the center of…