-
作者：Zhang, Fengshuo; Gao, Chao
作者单位：University of Chicago
摘要：We study convergence rates of variational posterior distributions for non-parametric and high-dimensional inference. We formulate general conditions on prior, likelihood and variational class that characterize the convergence rates. Under similar prior mass and testing conditions considered in the literature, the rate is found to be the sum of two terms. The first term stands for the convergence rate of the true posterior distribution, and the second term is contributed by the variational appr...
-
作者：Giordano, Francesco; Lahiri, Soumendra Nath; Parrella, Maria Lucia
作者单位：University of Salerno; North Carolina State University
摘要：We consider nonparametric regression in high dimensions where only a relatively small subset of a large number of variables are relevant and may have nonlinear effects on the response. We develop methods for variable selection, structure discovery and estimation of the true low-dimensional regression function, allowing any degree of interactions among the relevant variables that need not be specified a-priori. The proposed method, called the GRID, combines empirical likelihood based marginal t...
-
作者：Ekvall, Karl Oskar; Jones, Galin L.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full data. It requires neither that the data consist of independent observations, nor that the observations can be modeled as a stationary stochastic process. Compared to existing asymptotic theory using the idea of subsets, we substantially weaken the assumptions, b...
-
作者：Ghosal, Promit; Mukherjee, Sumit
作者单位：Columbia University
摘要：We study joint estimation of the inverse temperature and magnetization parameters (beta, B) of an Ising model with a nonnegative coupling matrix A(n) of size n x n, given one sample from the Ising model. We give a general bound on the rate of consistency of the bi-variate pseudo-likelihood estimator. Using this, we show that estimation at rate n(-1/2) is always possible if A(n) is the adjacency matrix of a bounded degree graph. If A(n) is the scaled adjacency matrix of a graph whose average de...
-
作者：Bravo, Francesco; Carlos Escanciano, Juan; Van Keilegom, Ingrid
作者单位：University of York - UK; Universidad Carlos III de Madrid; KU Leuven
摘要：In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks' theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities, and hence Wilks' theorem breaks down. This article suggests a general approach to restore Wilks' phenomenon in two-step semiparametric em...
