Search

Testing the equality for two-sample means with high dimensional distributions is a fundamental problem in statistics. In the past two decades, many efforts have been devoted to comparing the mean vectors of two populations. Many existing tests rely on naive diagonal or trace estimators of the covariance matrix, ignoring the dependence structure between variables. To make more use of the dependence structure, a new nonparametric test based on random selections is proposed to test the population mean vector of nonnormal high-dimensional multivariate data. This makes more efficient use of the covariance structure to deal with dependent variables. The asymptotic null distribution of the proposed test is standard normal, regardless of the parent distributions of the random samples and the relations between data dimensions and sample sizes. Extensive simulations show that the power performance of the proposed test is encouraging compared with some existing methods. [ABSTRACT FROM AUTHOR]

Data analysis based on information from different sources, typically known as the data fusion problem, is common in economic and biomedical studies. An interesting question concerns the regression of an outcome variable on certain covariates when combining two distinct datasets. These datasets consist of a primary sample containing the outcome and a subset of the covariates, and a supplemental sample comprising information only on the full set of covariates. Previous methods have proposed doubly robust estimation procedures that employ a single propensity score model for the data fusion process and a single imputation model for the covariates available only in the supplemental dataset. However, it may be questionable to assume that either model is correctly specified due to an unknown data generating process. To address this issue, an empirical likelihood based approach that calibrates multiple propensity scores and imputation models is introduced. The resulting estimator is consistent when any one of the models is correctly specified and is robust against extreme values of the fitted propensity scores. The asymptotic normality property and the estimation efficiency are also discussed. Simulation studies show that the proposed estimator has substantial advantages over existing estimators, and an assembled U.S. household expenditure data example is used for illustration. [ABSTRACT FROM AUTHOR]

Cui et al. (2015) proposed a mean–variance feature-screening method based on the index M V (X | Y). By modifying M V (X | Y) with a weight function, a new index A D (X , Y) is introduced to measure the dependence between X and Y , and a corresponding feature-screening procedure called Anderson–Darling sure independence screening (AD-SIS) is proposed for ultrahigh-dimensional discriminant analysis. The sure screening and ranking consistency properties are established under mild conditions. It is shown that AD-SIS is model free with no specification of model structure and can be applied to multi-classification. Furthermore, AD-SIS is robust against heavy-tailed distributions. As such, it can be used to identify the tail difference for the covariate's distribution. The finite-sample performance of AD-SIS is assessed by simulation and real data analysis. The results show that, compared with existing methods, AD-SIS can be more competitive for feature screening for ultrahigh-dimensional discriminant analysis. [ABSTRACT FROM AUTHOR]

Abstract: When there are many predictors, how to efficiently impute responses missing at random is an important problem to deal with for regression analysis because this missing mechanism, unlike missing completely at random, is highly related to high-dimensional predictor vectors. In sufficient dimension reduction framework, the fusion-refinement (FR) method in the literature is a promising approach. To make estimation more accurate and efficient, two methods are suggested in this paper. Among them, one method uses the observed data to help on missing data generation, and the other one is an ad hoc approach that mainly reduces the dimension in the nonparametric smoothing in data generation. A data-adaptive synthesization of these two methods is also developed. Simulations are conducted to examine their performance and a HIV clinical trial dataset is analyzed for illustration. [Copyright &y& Elsevier]

Abstract Under dimension reduction structure, several semiparametric estimators for the mean of missing response are proposed, which can efficiently deal with the dimensionality problem. Specifically, a generalized version of Augmented Inverse Probability Weighting estimator (AIPW) is proposed and its double robustness, estimation consistency and asymptotic efficiency are investigated. A generalized version of Inverse Probability Weighting (IPW) estimator is also introduced. An asymptotic efficiency reduction phenomenon occurs in the sense that the IPW estimator with the true selection probability is asymptotically less efficient than the one with an estimated selection probability. Besides, two partial imputation and two complete imputation estimators are discussed. We further systematically investigate the comparisons among these estimators in theory. Several simulation studies and a real data analysis are conducted for performance examination and illustration. [ABSTRACT FROM AUTHOR]

The Wilcoxon signed-rank test and the Wilcoxon-Mann-Whitney test are two commonly used rank-based methods for one- and two-sample tests when the one-dimensional data are not normally distributed. The new rank-based nonparametric tests for equality of mean vectors are proposed in the high-dimensional settings. To overcome the technical challenges in data sorting, the new statistics are constructed by taking the sum of the Wilcoxon signed-rank or Wilcoxon-Mann-Whitney test statistics from each dimension of the data. The asymptotic properties of the proposed test statistics are investigated under the null and local alternative hypotheses. Simulation studies show that the new tests perform as well as the state-of-the-art methods when the high-dimensional data are normally distributed, but they turn out to be more powerful when the normality assumption is violated. Finally, the new testing methods are also applied to a human peripheral blood mononuclear cells gene expression data set for demonstrating their usefulness in practice. [ABSTRACT FROM AUTHOR]