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1. Projection Test with Sparse Optimal Direction for High-Dimensional One Sample Mean Problem

   https://doi.org/10.1007/978-3-030-46161-4_19  

   Liu, W. ; Li, R. ( July 2020 , Contemporary Experimental Design, Multivariate Analysis and Data Mining)

   Fan, J ; Pan, J. (Ed.)

   Testing whether the mean vector from some population is zero or not is a fundamental problem in statistics. In the high-dimensional regime, where the dimension of data p is greater than the sample size n, traditional methods such as Hotelling’s T2 test cannot be directly applied. One can project the high-dimensional vector onto a space of low dimension and then traditional methods can be applied. In this paper, we propose a projection test based on a new estimation of the optimal projection direction Σ^{−1}μ. Under the assumption that the optimal projection Σ^{−1}μ is sparse, we use a regularized quadratic programming with nonconvex penalty and linear constraint to estimate it. Simulation studies and real data analysis are conducted to examine the finite sample performance of different tests in terms of type I error and power. 

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2. Testing and Confidence Intervals for High Dimensional Proportional Hazards Models

   https://doi.org/10.1111/rssb.12224  

   Fang, Ethan_X ; Ning, Yang ; Liu, Han ( December 2016 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

   The paper considers the problem of hypothesis testing and confidence intervals in high dimensional proportional hazards models. Motivated by a geometric projection principle, we propose a unified likelihood ratio inferential framework, including score, Wald and partial likelihood ratio statistics for hypothesis testing. Without assuming model selection consistency, we derive the asymptotic distributions of these test statistics, establish their semiparametric optimality and conduct power analysis under Pitman alternatives. We also develop new procedures to construct pointwise confidence intervals for the baseline hazard function and conditional hazard function. Simulation studies show that all tests proposed perform well in controlling type I errors. Moreover, the partial likelihood ratio test is empirically more powerful than the other tests. The methods proposed are illustrated by an example of a gene expression data set.

    

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3. Robust Tests for Treatment Effect in Survival Analysis under Covariate-Adaptive Randomization

   https://doi.org/10.1111/rssb.12392  

   Ye, Ting ; Shao, Jun ( August 2020 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Covariate-adaptive randomization is popular in clinical trials with sequentially arrived patients for balancing treatment assignments across prognostic factors that may have influence on the response. However, existing theory on tests for the treatment effect under covariate-adaptive randomization is limited to tests under linear or generalized linear models, although the covariate-adaptive randomization method has been used in survival analysis for a long time. Often, practitioners will simply adopt a conventional test to compare two treatments, which is controversial since tests derived under simple randomization may not be valid in terms of type I error under other randomization schemes. We derive the asymptotic distribution of the partial likelihood score function under covariate-adaptive randomization and a working model that is subject to possible model misspecification. Using this general result, we prove that the partial likelihood score test that is robust against model misspecification under simple randomization is no longer robust but conservative under covariate-adaptive randomization. We also show that the unstratified log-rank test is conservative and the stratified log-rank test remains valid under covariate-adaptive randomization. We propose a modification to variance estimation in the partial likelihood score test, which leads to a score test that is valid and robust against arbitrary model misspecification under a large family of covariate-adaptive randomization schemes including simple randomization. Furthermore, we show that the modified partial likelihood score test derived under a correctly specified model is more powerful than log-rank-type tests in terms of Pitman’s asymptotic relative efficiency. Simulation studies about the type I error and power of various tests are presented under several popular randomization schemes.

    

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4. Tests for High Dimensional Generalized Linear Models

   https://doi.org/10.1111/rssb.12152  

   Guo, Bin ; Chen, Song_Xi ( January 2016 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

   We consider testing regression coefficients in high dimensional generalized linear models. By modifying the test statistic of Goeman and his colleagues for large but fixed dimensional settings, we propose a new test, based on an asymptotic analysis, that is applicable for diverging dimensions and is robust to accommodate a wide range of link functions. The power properties of the tests are evaluated asymptotically under two families of alternative hypotheses. In addition, a test in the presence of nuisance parameters is also proposed. The tests can provide p-values for testing significance of multiple gene sets, whose application is demonstrated in a case-study on lung cancer.

    

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5. Assessing Fit in Ordinal Factor Analysis Models: SRMR vs. RMSEA

   https://doi.org/10.1080/10705511.2019.1611434  

   Shi, D ; Maydeu-Olivares, A. ; Rosseel, Y. ( January 2019 , Structural equation modeling)

   This study introduces the statistical theory of using the Standardized Root Mean Squared Error (SRMR) to test close fit in ordinal factor analysis. We also compare the accuracy of confidence intervals (CIs) and tests of close fit based on the Standardized Root Mean Squared Error (SRMR) with those obtained based on the Root Mean Squared Error of Approximation (RMSEA). We use Unweighted Least Squares (ULS) estimation with a mean and variance corrected test statistic. The current (biased) implementation for the RMSEA never rejects that a model fits closely when data are binary and almost invariably rejects the model in large samples if data consist of five categories. The unbiased RMSEA produces better rejection rates, but it is only accurate enough when the number of variables is small (e.g., p = 10) and the degree of misfit is small. In contrast, across all simulated conditions, the tests of close fit based on the SRMR yield acceptable type I error rates. SRMR tests of close fit are also more powerful than those using the unbiased RMSEA. 

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