Reseach in Statistics and Mathematics …

I have extensive interests and expertise in Statistics and Mathematics. My main research area is simultaneous inference for high-dimensional dependent data and for high-dimensional discrete data. I have also worked on mathematical problems on Ito diffusion processes, time series models, probability, and complex analysis.

Information on Some Projects

Please click on research document for some details (less than given in the preprints but more than given by the abstracts) on some projects listed below.

Projects in Statistics

  1. Estimating the proportion of true null hypotheses or false null hypotheses

    1. Under strong covariance dependence

      1. Xiongzhi Chen and R.W. Doerge (2014): A consistent estimator of the proportion of nonzero Normal means under certain strong covariance dependence. Preprint.

    2. Under independence

      1. Xiongzhi Chen and John D. Storey (2014): Estimating the proportion of true null hypotheses via goodness of fit. Mansucript.

  2. False discoverate rate (FDR) procedures

    1. Under independence but mainly for discrete and heterogeneous null distributions

      1. Xiongzhi Chen and R.W. Doerge (2015): A weighted FDR procedure under discrete and heterogeneous null distributions. Preprint; R package ‘‘fdrDiscreteNull’’ on CRAN.

      2. Xiongzhi Chen and R.W. Doerge (2014): Generalized estimators for multiple testing: proportion of true nulls and false discovery rate. Preprint; R package ‘‘fdrDiscreteNull’’ on CRAN.

    2. Under independence but for continuous and homogeneous null distributions

      1. Xiongzhi Chen, David G. Robinson and John D. Storey (2014): Functional false discovery rate with application to genomics. Manuscript.

  3. Simultaneous estimation and inference

    1. Without a linear trend but under exogeneity

      1. Xiongzhi Chen and John D. Storey (2014): Consistent estimation of low-dimensional latent structure in high-dimensional data. Preprint.

    2. With a linear trend but under exogeneity

      1. John D. Storey, Keyur H. Desai and Xiongzhi Chen (2013): Empirical Bayes inference of dependent high-dimensional data. Manuscript.

      2. Xiongzhi Chen and John D. Storey (2014): Nonparametric empirical Bayes estimation of the surrogate variable analysis model. Manuscript.

    3. With a linear trend but under endogeneity

      1. Xiongzhi Chen, Wei Hao and John D. Storey: Regression herding. In preparation.

  4. Multiple testing from the perspective of stochastic processes

    1. Xiongzhi Chen and R.W. Doerge (2014): A strong law of larger numbers related to multiple testing normal means. Preprint.

    2. Xiongzhi Chen and R.W. Doerge (2015): Stopping time property of thresholds of Storey-type FDR procedures. Preprint.

Projects in Mathematics

  1. Theory on one-parameter natural exponential families (NEFs)

    1. Xiongzhi Chen (2016): Resolution of a conjecture on variance functions for one-parameter natural exponential family. Statistics and Probability Letters.

    2. Xiongzhi Chen (2015): Reduction functions for the variance function of one-parameter natural exponential family. Preprint.

  2. Time series models

    1. Xiongzhi Chen (2015): Explicit solutions to a vector time series model and its induced model for business cycles. Preprint.

  3. Diffusion processes: modelling and estimation

    1. Master's Thesis

  4. Geometric probability

    1. Xiongzhi Chen (2015+): On Samuel Karlin's problem of geometric probability and a variant. In prepartion.

  5. Neural networks

    1. Xiongzhi Chen and Changlin Cai (2006): A new architecture for multilayer perceptrons as function approximators. Natural Science Edition, Journal of Sichuan University, Vol. 2.

    2. Changlin Cai, Zhongzhi Shi, Xiongzhi Chen (2006): The Fisher information matrix on neural manifolds of multilayer perceptrons. Natural Science Edition, Journal of Sichuan University, Accepted. pdf.

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