基于Besicovitch定理的条件期望的蒙特卡罗近似方法--应用于一般半正态分布参数的等变估计
A Monte Carlo Method to Approximate Conditional Expectations based on a Theorem of Besicovitch: Application to Equivariant Estimation of the Parameters of the General Half-Normal Distribution
摘要：
一个自然的蒙特卡罗方法来近似条件期望的概率框架是合理的启发贝西科维奇覆盖定理微分措施的一般结果。当密度不可用或不容易计算时，该方法特别有用。该方法是通过一些例子来说明，也可以用于统计设置，以近似的条件期望给定的充分统计量，例如。事实上，它被应用于评估一般半正态分布的位置参数的最小风险同变估计（MRE），因为该估计是根据位置和尺度参数的已知值的条件期望来描述的。为了完备性，给出了尺度参数的最小风险同变估计的显式表达式。据我们所知，这些估计还没有在文献中给出。仿真研究实现了这些估计的行为与极大似然和无偏估计量。
英文摘要：
A natural Monte Carlo method to approximate conditional expectations in a probabilistic framework is justified by a general result inspired on the Besicovitch covering theorem on differentiation of measures. The method is specially useful when densities are not available or are not easy to compute. The method is illustrated by means of some examples and can also be used in a statistical setting to approximate the conditional expectation given a sufficient statistic, for instance. In fact, it is applied to evaluate the minimum risk equivariant estimator (MRE) of the location parameter of a general half-normal distribution since this estimator is described in terms of a conditional expectation for known values of the location and scale parameters. For the sake of completeness, an explicit expression of the the minimum risk equivariant estimator of the scale parameter is given. For all we know, these estimators have not been given before in the literature. Simulation studies are realized to compare the behavior of these estimators with that of maximum likelihood and unbiased estimators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
