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利用非参数回归估计变点AI 解读

We consider a regression model in which the mean function may have a discontinuity at an unknown point. We propose an estimate of the location of the discontinuity based on one-side nonparametric regression estimates of the mean function. The change point estimate is shown to converge in probability at rate $O(n^{-1})$ and to have the same asymptotic distribution as maximum likelihood estimates considered by other authors under parametric regression models. Confidence…

泊松过程变化点的对数线性模型AI 解读

Many methods have been proposed for modelling nonhomogeneous Poisson processes, including change point models and log-linear models. In this paper, we use likelihood ratio tests to choose which of these models are necessary. Of particular interest is the test for the presence of a change point, for which standard asymptotic theory is not valid. Large deviation methods are applied to approximate the significance level, and power approximations are given. Confidence regions…