It is important to study the convergence rates of the misclassification error as n tends to infinity. It is known that such a rate can't exist for the set of all distributions. In this paper we obtain the optimal convergence rates for a class of distributions D~(λ,ω) in multicategory ...
It is known that such a rate can't exist for the set of all distributions. In this paper we obtain the optimal convergence rates for a class of distributions D(λ,ω) in multicategory classification and nonstandard binary classification. Key words rate of convergence / error probability /...
如果一个问题的minimax lower bound convergence rate是根号n，那对应的白话翻译是“不存在这样的一个esti...
Brown, Levine and Wang [1] also obtained a uniform over a Lipschitz ball Λα(M) convergence result for an estimator of the functional component, establishing the rate of convergence n−2α/(2α+q). To the best of our knowledge, the optimal in the minimax sense rate of convergence ...
Optimal rate of convergenceCovariance structure plays an important role in high-dimensional statistical inference. In a range of applications including imaging analysis and fMRI studies, random variables are observed on a lattice graph. In such a setting, it is important to account for the lattice ...
When Q satisfies the margin assumption with the parameter \alpha, defined in Section 2, and \eta_Q(x) belongs to the \left(\beta, C_\beta\right)-Hölder function class, it is shown that, under the regularity conditions, the minimax optimal rate of convergence is given by \inf _{\...
It is a method proposed more than thirty years ago, but somehow there has not been any theoretic result on its convergence rate in the literature. In this paper, we fill the gap by establishing minimax optimal convergence rates for Dawid-Skene estimator. We obtain a lower bound which holds ...
We find that the rate of convergence depends on the class of optimization algorithms used to solve the approximate problem as well as the policy for selecting discretization level and number of optimization iterations. We construct optimal policies that achieve the best possible rate of convergence ...
The optimal rates of convergence are of logarithmic type under additional constraints on the small ball probabilities and entropy. We assume that the mode is contained in some totally bounded set and use covering methods to define a mode estimator and deduce strong consistency and rate optimality....
[公式]统计中一般指的是所有estimator中最快rate of convergence。举个例子要估计mean，我们用sample aver...