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回应讨论：当变量数远大于样本量时的 Dantzig 选择器统计估计AI 解读

First of all, we would like to thank all the discussants for their interest and comments, as well as for their thorough investigation.The comments all underlie the importance and timeliness of the topics discussed in our paper, namely, accurate statistical estimation in high dimensions.We would also like to thank the editors for this opportunity to comment briefly on a few issues raised in the discussions.Of special interest is the diversity of perspectives, which include…

Dantzig 选择器：变量数远大于样本量时的统计估计AI 解读

In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y=Xβ+z, where β∈Rp is a parameter vector of interest, X is a data matrix with possibly far fewer rows than columns, n≪p, and the zi’s are i.i.d. N(0, σ2). Is it possible to estimate β reliably based on the noisy data y? To estimate β, we introduce a new estimator—we call it the Dantzig selector—which is a…

核密度估计与局部似然密度估计的相对效率AI 解读

Summary Local likelihood methods enjoy advantageous properties, such as good performance in the presence of edge effects, that are rarely found in other approaches to nonparametric density estimation. However, as we argue in this paper, standard kernel methods can have distinct advantages when edge effects are not present. We show that, whereas the integrated variances of the two methods are virtually identical, the integrated squared bias of a conventional kernel estimator…