This proposal develops novel statistical methods to select a small group of molecules from high-throughput data such as microarray, proteomic, and next generation sequence from biomedical research, especially for autism studies and brain tumors. It focuses on developing efficient methods and valid statistical tools for controlling false discovery rate an testing treatment effects on a group of molecules, for feature selection and model building in presence of errors-in-variables, endogeneity, and heavy-tail error distributions, and for predicting clinical outcomes and understanding molecular mechanisms. It develops semiparametric and nonparametric models to reduce modeling biases and to augment features. It furthers the developments on estimating large covariance matrices for understanding genetic network, statistical model building and inferences. It introduces multivariate independence screening and conditional independence screening techniques to reduce false negatives and false positives in variable screening, and develops computable and optimal penalized likelihood methods for an array of statistical models. The strength and weakness of each proposed method will be critically analyzed via theoretical investigations and simulation studies. Related software will be developed. Data sets from ongoing autism research, brain tumor, and other biomedical studies will be analyzed using the newly developed methods and the results will be further biologically confirmed and investigated. The research findings will have strong impact on statistical analysis of high throughput data for biomedical research and on understanding molecular mechanisms of autism, brain tumors, and other diseases.
This proposal develops novel statistical and bioinformatic tools for finding genes, proteins, and SNPs that are associated with clinical outcomes. Data sets from ongoing autism research, brain tumors and other biomedical studies will be critically analyzed using the newly developed statistical and bioinformatic methods, and the results will be further biologically confirmed and investigated. The research findings will have strong impact on understanding molecular mechanisms of autism, brain tumors, and other diseases and developing therapeutic targets.
|Fan, Jianqing; Liu, Han; Wang, Weichen (2018) LARGE COVARIANCE ESTIMATION THROUGH ELLIPTICAL FACTOR MODELS. Ann Stat 46:1383-1414|
|Chen, Zhao; Fan, Jianqing; Li, Runze (2018) Error Variance Estimation in Ultrahigh-Dimensional Additive Models. J Am Stat Assoc 113:315-327|
|Li, Quefeng; Cheng, Guang; Fan, Jianqing et al. (2018) Embracing the Blessing of Dimensionality in Factor Models. J Am Stat Assoc 113:380-389|
|Fan, Jianqing; Shao, Qi-Man; Zhou, Wen-Xin (2018) ARE DISCOVERIES SPURIOUS? DISTRIBUTIONS OF MAXIMUM SPURIOUS CORRELATIONS AND THEIR APPLICATIONS. Ann Stat 46:989-1017|
|Battey, Heather; Fan, Jianqing; Liu, Han et al. (2018) DISTRIBUTED TESTING AND ESTIMATION UNDER SPARSE HIGH DIMENSIONAL MODELS. Ann Stat 46:1352-1382|
|Zhou, Wen-Xin; Bose, Koushiki; Fan, Jianqing et al. (2018) A NEW PERSPECTIVE ON ROBUST M-ESTIMATION: FINITE SAMPLE THEORY AND APPLICATIONS TO DEPENDENCE-ADJUSTED MULTIPLE TESTING. Ann Stat 46:1904-1931|
|Fan, Jianqing; Liu, Han; Sun, Qiang et al. (2018) I-LAMM FOR SPARSE LEARNING: SIMULTANEOUS CONTROL OF ALGORITHMIC COMPLEXITY AND STATISTICAL ERROR. Ann Stat 46:814-841|
|Avella-Medina, Marco; Battey, Heather S; Fan, Jianqing et al. (2018) Robust estimation of high-dimensional covariance and precision matrices. Biometrika 105:271-284|
|Aït-Sahalia, Yacine; Fan, Jianqing; Laeven, Roger J A et al. (2017) Estimation of the Continuous and Discontinuous Leverage Effects. J Am Stat Assoc 112:1744-1758|
|Wang, Weichen; Fan, Jianqing (2017) Asymptotics of empirical eigenstructure for high dimensional spiked covariance. Ann Stat 45:1342-1374|
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