Random weighting estimation of sampling distributions via importance resampling

This paper presents a new random weighting-based adaptive importance resampling method to estimate the sampling distribution of a statistic. A random weighting-based cross-entropy procedure is developed to iteratively calculate the optimal resampling probability weights by minimizing the Kullback-Leibler distance between the optimal importance resampling distribution and a family of parameterized distributions. Subsequently, the random weighting estimation of the sampling distribution is constructed from the obtained optimal importance resampling distribution. The convergence of the proposed method is rigorously proved. Simulation and experimental results demonstrate that the proposed method can effectively estimate the sampling distribution of a statistic.