-
作者：Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; Hiroshima University
摘要：In this paper, we study the problem of estimating the number of significant components in principal component analysis (PCA), which corresponds to the number of dominant eigenvalues of the covariance matrix of p variables. Our purpose is to examine the consistency of the estimation criteria AIC and BIC based on the model selection criteria by Akaike [In 2nd International Symposium on Information Theory (1973) 267-281, Akademia Kiado] and Schwarz [Estimating the dimension of a model 6 (1978) 46...
-
作者：Bellec, Pierre C.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); Rutgers University System; Rutgers University New Brunswick; Institut Polytechnique de Paris; ENSAE Paris
摘要：The performance of Least Squares (LS) estimators is studied in shape-constrained regression models under Gaussian and sub-Gaussian noise. General bounds on the performance of LS estimators over closed convex sets are provided. These results have the form of sharp oracle inequalities that account for the model misspecification error. In the presence of misspecification, these bounds imply that the LS estimator estimates the projection of the true parameter at the same rate as in the well-specif...
-
作者：Lin, Qian; Zhao, Zhigen; Liu, Jun S.
作者单位：Tsinghua University; Harvard University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：We provide here a framework to analyze the phase transition phenomenon of slice inverse regression (SIR), a supervised dimension reduction technique introduced by Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]. Under mild conditions, the asymptotic ratio rho = lim p/n is the phase transition parameter and the SIR estimator is consistent if and only if rho = 0. When dimension p is greater than n, we propose a diagonal thresholding screening SIR (DT-SIR) algorithm. This method provides us with ...
-
作者：Amini, Arash A.; Levina, Elizaveta
作者单位：University of California System; University of California Los Angeles; University of Michigan System; University of Michigan
摘要：The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves a computationally infeasible optimization problem. We propose a new semidefinite programming (SDP) solution to the problem of fitting the SBM, derived as a relaxation of the MLE. We put ours and previously proposed SDPs in a unified framework, as relaxations of the MLE over various subclasses of the SBM, which also reveals a connection to the well-known pr...
-
作者：Li, Xiaoou; Liu, Jingchen; Ying, Zhiliang
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Columbia University
摘要：The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses are considered [In Proc. 4th Berkeley Sympos. Math. Statist. and Prob. (1961) 105-123; J. Roy. Statist. Soc. Ser. B 24 (1962) 406-424]. The significance level is set such that the maximal type I and type II error probabilities for the generalized likelihood ra...
-
作者：Chen, Mengjie; Gao, Chao; Ren, Zhao
作者单位：University of Chicago; University of Chicago; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of covariance matrices, but are also robust to outliers from arbitrary sources. In this paper, we define a new concept called matrix depth and then propose a robust covariance matrix estimator by maximizing the empirical depth function. The proposed estimator is sh...
-
作者：Fan, Jianqing; Shao, Qi-Man; Zhou, Wen-Xin
作者单位：Fudan University; Princeton University; Princeton University; Chinese University of Hong Kong; University of California System; University of California San Diego
摘要：Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries from these data mining approaches be spurious due to high dimensionality and limited sample size? Can our fundamental assumptions about the exogeneity of the covariates needed for such variable selection be validated with the data? To answer these questions, we need to derive the distribution...
-
作者：Tibshirani, Ryan J.; Rinaldo, Alessandro; Tibshirani, Rob; Wasserman, Larry
作者单位：Carnegie Mellon University; Carnegie Mellon University; Stanford University
摘要：Recently, Tibshirani et al. [J. Amer. Statist. Assoc. 111 (2016) 600-620] proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this method, without assuming normality. We prove that the test statistic of Tibshirani et al. (2016) is asymptotically valid, as the number of samples n grows and the dimension d of the regression problem stays fixed. Our asym...
-
作者：Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; Hiroshima University
摘要：In this paper, we derive the asymptotic joint distributions of the eigenvalues under the null case and the local alternative cases in the MANOVA model and multiple discriminant analysis when both the dimension and the sample size are large. Our results are obtained by random matrix theory (RMT) without assuming normality in the populations. It is worth pointing out that the null and nonnull distributions of the eigenvalues and invariant test statistics are asymptotically robust against departu...
-
作者：Paparoditis, Efstathios
作者单位：University of Cyprus
摘要：A bootstrap procedure for functional time series is proposed which exploits a general vector autoregressive representation of the time series of Fourier coefficients appearing in the Karhunen Loeve expansion of the functional process. A double sieve-type bootstrap method is developed, which avoids the estimation of process operators and generates functional pseudo time series that appropriately mimics the dependence structure of the functional time series at hand. The method uses a finite set ...
