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Estimating linear functionals of a sparse family of Poisson means. (arXiv:1712.01775v2 [math.ST] UPDATED)
来源于:arXiv
Assume that we observe a sample of size n composed of p-dimensional signals,
each signal having independent entries drawn from a scaled Poisson distribution
with an unknown intensity. We are interested in estimating the sum of the n
unknown intensity vectors, under the assumption that most of them coincide with
a given 'background' signal. The number s of p-dimensional signals different
from the background signal plays the role of sparsity and the goal is to
leverage this sparsity assumption in order to improve the quality of estimation
as compared to the naive estimator that computes the sum of the observed
signals. We first introduce the group hard thresholding estimator and analyze
its mean squared error measured by the squared Euclidean norm. We establish a
nonasymptotic upper bound showing that the risk is at most of the order of
{\sigma}^2(sp + s^2sqrt(p)) log^3/2(np). We then establish lower bounds on the
minimax risk over a properly defined class of collections of s-sparse sign 查看全文>>