We consider the problem of locating a jump discontinuity (change-point) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding responses. Budget constraints dictate that a total of $n$ such measurements can be obtained. A multistage adaptive procedure is proposed, where at each stage an estimate of the change point is obtained and new points are sampled from its appropriately chosen neighborhood. It is shown that such procedures accelerate the rate of convergence of the least squares estimate of the change-point. Further, the asymptotic distribution of the estimate is derived using empirical processes techniques. The latter result provides guidelines on how to choose the tuning parameters of the multistage procedure in practice. The improved efficiency of the procedure is demonstrated using real and synthetic data. This problem is primarily motivated by applications in engineering systems.
Approximate Shapley value estimation using sampling without replacement and variance estimation via the new Symmetric bootstrap and the Doubled half bootstrap
Consistency of the Adaptive Multiple Importance Sampling
在蒙特卡罗技术中，重要性抽样需要对建议分布进行微调，这现在可以通过迭代方案顺利解决。Cornuet等人（2012）的自适应多重要性抽样（AMIS）由于引入了回收程序，在稳定性和有效样本量方面提供了显著改善。然而，非盟特派团信息系统估计数的一致性在很大程度上仍然没有定论。在这项工作中，我们证明了AMIS的收敛性，在学习过程中略有修改的成本。与Douc et al.（2007 a）相反，这里的结果是在渐近状态下得到的，其中迭代次数趋于无穷大，而每次迭代的绘图次数是固定的，但整数序列不断增长。因此，在最后一个政权的自适应人口蒙特卡罗算法的一些结果揭示了新的光。
