Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation

We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated coordinates. The first test is constructed by carrying out thresholding to remove the non-signal bearing dimensions. The second test combines data transformation via the precision matrix with the thresholding. The benefits of the thresholding and the data transformations are showed by a reduced variance of the test thresholding statistics, the improved power and a wider detection region of the tests. Simulation experiments and an empirical study are performed to confirm the theoretical findings and to demonstrate the practical implementations.Comment: 64 page

Tests alternative to higher criticism for high-dimensional means under sparsity and column-wise dependence

We consider two alternative tests to the Higher Criticism test of Donoho and Jin [Ann. Statist. 32 (2004) 962-994] for high-dimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise dependence. The two alternative test statistics are constructed by first thresholding $L_1$ and $L_2$ statistics based on the sample means, respectively, followed by maximizing over a range of thresholding levels to make the tests adaptive to the unknown signal strength and sparsity. The two alternative tests can attain the same detection boundary of the Higher Criticism test in [Ann. Statist. 32 (2004) 962-994] which was established for uncorrelated Gaussian data. It is demonstrated that the maximal $L_2$-thresholding test is at least as powerful as the maximal $L_1$-thresholding test, and both the maximal $L_2$ and $L_1$-thresholding tests are at least as powerful as the Higher Criticism test.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1168 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Empirical Likelihood Ratio Tests for Coe cients in High Dimensional Heteroscedastic Linear Models

This paper considers hypothesis testing problems for a low-dimensional coefficient vector in a high-dimensional linear model with heteroscedastic variance. Heteroscedasticity is a commonly observed phenomenon in many applications, including finance and genomic studies. Several statistical inference procedures have been proposed for low-dimensional coefficients in a high-dimensional linear model with homoscedastic variance, which are not applicable for models with heteroscedastic variance. The heterscedasticity issue has been rarely investigated and studied. We propose a simple inference procedure based on empirical likelihood to overcome the heteroscedasticity issue. The proposed method is able to make valid inference even when the conditional variance of random error is an unknown function of high-dimensional predictors. We apply our inference procedure to three recently proposed estimating equations and establish the asymptotic distributions of the proposed methods. Simulation studies and real data applications are conducted to demonstrate the proposed methods

Unified empirical likelihood ratio tests for functional concurrent linear models and the phase transition from sparse to dense functional data

We consider the problem of testing functional constraints in a class of functional concurrent linear models where both the predictors and the response are functional data measured at discrete time points. We propose test procedures based on the empirical likelihood with bias‐corrected estimating equations to conduct both pointwise and simultaneous inferences. The asymptotic distributions of the test statistics are derived under the null and local alternative hypotheses, where sparse and dense functional data are considered in a unified framework. We find a phase transition in the asymptotic null distributions and the orders of detectable alternatives from sparse to dense functional data. Specifically, the tests proposed can detect alternatives of √n‐order when the number of repeated measurements per curve is of an order larger than urn:x-wiley:13697412:media:rssb12246:rssb12246-math-0001 with n being the number of curves. The transition points urn:x-wiley:13697412:media:rssb12246:rssb12246-math-0002 for pointwise and simultaneous tests are different and both are smaller than the transition point in the estimation problem. Simulation studies and real data analyses are conducted to demonstrate the methods proposed

Rotective effect of Fengliao-Changweikang extracts, a traditional Chinese herbal medicine formula,on mucosa in rat with chronic gastritis

Background: Fengliao-Changwei-Kang(FCK), the Chinese patent drug, is a famous traditional Chinese herbal medicine formula. It has a significant effect on the clinic treatment of gastrointestinal diseases  including gastritis, enteritis and diarrhea for many years. However, there is few research on the  protective effects of FCK on the gastric mucosa of chronic gastritis (CG) model rat. Objective: The present study aimed to explore the effects of FCK extract on mucosa in rats with Chronic Gastritis.Materials and Methods: 50 SD mice were randomly divided into 5 groups with 10 in each group（five per sex). The groups are respectively control group, model group, low, middle and high FCK extracts (FCK I, II and III) group. The CG rat model was induced by synthetic methods. FCK I, II and III group were  administrated with FCK extracts at 2.16g• kg, 4.32g• kg, 8.94g• kg once per day for 21 consecutive  days, and the control group and model group were administrated the same volume of distilled water at 10mL/kg once per day. 16 hours after the last administration, the rats were anesthetized and their blood and stomach were drawn from vena cava and abdominal cavity. The serum levels of EGF was measured by enzyme linked immunosorbent assay(ELISA) method, the expression of growth factor receptor (EGFR) in gastric mucosa was detected by immunohistochemical method, and the mRNA expressions of NF-κB p65 was detected in-situ hybridization.Results: The inflammation grades and the expressions of NF-κB p65 mRNA in gastric mucosa of the model group were markedly higher than those of the control group (P<0.05). The inflammation grades of gastric mucosa and the expressions of NF-κB p65 mRNA in gastric mucosa the FCK extract group are significantly lower than those of the model group, and the FCK extract group at 8.64g/kg could greatly increase the serum levels of EGF and the expressions of EGFR in gastric mucosa. High EGF level was found in FCK extract group at 4.32g/kg, but low in FCK extract groups at 2.16g/kg. There were no marked differences among the rats from control group, model group and FCK extract group on ratio of Ll/L2 (P>0.05).Conclusions: FCK extract could alleviate mucosal inflammation by down regulating the expressions of NF-κB p65 mRNA and promote tissue repair by up regulating EGFR expression in gastric mucosa cell.Keywords: chronic gastritis; fengliao-changwei-kang extract; epidermal growth factor receptor; nuclear factor kappa B

DEVELOPMENT AND APPLICATION OF A SIMULATED ALTITUDE CABIN

The purpose of this study was to examine the techniques of simulated altitude cabin developed by the Shandong Sports Science Center, China. Blood lactate of two male and two female long distance taking the contrast test of the same exercise load of Monark 829 bicycle and treadmill both in and out of the cabin was measured. Hemoglobin of four elite walk runners who lived in the cabin with the altitude of 3,000m for 14 hours every day and took the training out of the cabin in the rest of the time was also measured. Results showed that the value of blood lactate for same athlete after exercise load in the cabin is obviously higher than those outside of cabin, and that the mean value of hemoglobin of the four elite athletes increased 1.3g/dl before and after the test. It is concluded that the manufacture of the simulated altitude cabin is successful in simulating actual altitude training