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作者：Dette, Holger; Schorning, Kirsten
作者单位：Ruhr University Bochum
摘要：We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non-standard design problem and for some commonly used dose response models optimal designs are found expl...
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作者：Ma, Shujie; He, Xuming
作者单位：University of California System; University of California Riverside; University of Michigan System; University of Michigan
摘要：Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients. We consider a pseudo-profile likelihood approach to estimation and testing for single-index quantile regression models. We establish the asymptotic normality of the index coefficient estimator as well as the optimal convergence rate of the nonparametric function estimation. Moreover, we propose a score test for the index...
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作者：Doss, Charles R.; Wellner, Jon A.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Washington; University of Washington Seattle
摘要：We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and s-concave densities on R. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than n(-2/5) when -1 < s < infinity where s = 0 corresponds to the log-concave case. We also show that the MLE does not exist for the classes of s-concave densities with s < -1.
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作者：Han, Qiyang; Wellner, Jon A.
作者单位：University of Washington; University of Washington Seattle
摘要：In this paper, we study the approximation and estimation of s-concave densities via Renyi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist. 38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show continuity of the divergence functional in Q: if Q(n) -> Q in the Wasserstein metric, then the projec...
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作者：Massam, Helene; Wesolowski, Jacek
作者单位：York University - Canada; Warsaw University of Technology
摘要：In this paper, we first develop a new family of conjugate prior distributions for the cell probability parameters of discrete graphical models Markov with respect to a set P of moral directed acyclic graphs with skeleton a given decomposable graph G. This family, which we call the P-Dirichlet, is a generalization of the hyper Dirichlet given in [Ann. Statist. 21 (1993) 12721317]: it keeps the directed strong hyper Markov property for every DAG in P but increases the flexibility in the choice o...
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作者：Lam, Clifford
作者单位：University of London; London School Economics & Political Science
摘要：We introduce nonparametric regularization of the eigenvalues of a sample covariance matrix through splitting of the data (NERCOME), and prove that NERCOME enjoys asymptotic optimal nonlinear shrinkage of eigenvalues with respect to the Frobenius norm. One advantage of NERCOME is its computational speed when the dimension is not too large. We prove that NERCOME is positive definite almost surely, as long as the true covariance matrix is so, even when the dimension is larger than the sample size...
