NA样本均值的随机加权估计及应用

Applying Random Weighting Method to Estimating NA Dependent Sample Mean

研究了随机变量序列{Xn,n≥1}为NA相协样本条件下,均值X-n的随机加权逼近。用n(Hk(x)-X-n)的条件分布去模拟n(X-n-μ)的分布,证明了该分布的随机加权逼近及其收敛性,并对研究结果进行了仿真分析。

Aim. Ref. 3 authored by Yu proposed the estimation of NA （negative association） dependent sample mean by using Bootstrap approximation method. Ref. 4 authored by Zheng pointed out that Random weighting approximation is better than Bootstrap approximation. In the full paper, we explain in some detail how to apply random weighting approximation method to estimating NA dependent sample mean and then use a numerical example to show that random weighting approximation method is indeed better than Bootstrap approximation method. The first topic is. random weighting approximation method for estimating NA dependent sample mean and its consistency. In the first topic, we give a mathematical proof, including a theorem, for the consistency of the random weighting approximation. The second topic is. simulations results and their analysis. In this topic, we use the random weighting approximation method and the Bootstrap approximation method respectively to simulate the estimation of the data measured by two gyros. The simulation results, shown in Fig. 1 and 2 in the full paper, indicate preliminarily that the estimation of the data with the random weighting method is highly accurate and indeed better than the Bootstrap approximation method.