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函数型数据序列的贪心分割AI 解读

We present a new approach known as greedy segmentation (GS) to identify multiple changepoints for a functional data sequence. The proposed multiple changepoint detection criterion links detectability with the projection onto a suitably chosen subspace and the changepoint locations. The changepoint estimator identifies the true changepoints for any predetermined number of changepoint candidates, either over-reporting or under-reporting. This theoretical finding supports the…

利用最大非线性条件相关检验条件独立AI 解读

In this paper, the maximal nonlinear conditional correlation of two random vectors X and Y given another random vector Z, denoted by ρ1(X, Y|Z), is defined as a measure of conditional association, which satisfies certain desirable properties. When Z is continuous, a test for testing the conditional independence of X and Y given Z is constructed based on the estimator of a weighted average of the form ∑k=1nZfZ(zk)ρ12(X, Y|Z = zk), where fZ is the probability density function…

后验分布的收敛速度与自适应估计AI 解读

The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so that the posterior distributions converge at the optimal rate without prior knowledge of the degree of smoothness of the density function or the regression function to be estimated.