I am currently interested in these research problems:
Empirical likelihood ratio method, and in particula, its applications in statistical analysis of censored survival data.
Testing and confidence intervals for AUC and pAUC by empirical likelihood method. (that is Area Under ROC Curve).
Computational methods for the Empirical Likelihood Ratio.
Survival Analysis. Restricted Mean Survival Time, and properties of the classic Kaplan-Meier estimator.
High dimensional regression problems (large p, small n).
LASSO and similar techniques applied to AFT models.
Buckley-James estimator; Cox models (and its extensions) and quantile regressions.
Regression models for ranking data --- improving the Bradley-Terry
model
(K ranking at a time). Scaling.
Statistical analysis for doubly censored data --- computation of
the distribution estimator, testing and confidence intervals.
I have also worked on the problems related to
Nonparametric Bayes estimator of survival curve with arbitrary
censored data,
Some of my researches were supported by grants from NSF and NIH.
Old Thesis of Li Lee (1990) at Columbia University (Adviser: John Morgan).
Thesis Abstract (one page). Freeness and Discreteness of Actions on R-trees by Finitely Generated Free Groups.
Old Thesis, Pre-prints, re-prints and updates.
Zhou, Mai (1986) Ph.D. Thesis. SOME NONPARAMETRIC TWO SAMPLE TESTS WITH RANDOMLY RIGHT CENSORED DATA
The
results concern mean based two sample tests with right censored
data, are still relevant. But the original Dissertation is only
available in paper form/hard copy at Columbia University library. I
scanned part of the Dissertation here, so that they are available in
digital form. Hopefully, more people can read it over internet.
Wang, W. and Zhou, M. (1995). Iterative Least Squares Estimator of Binary Choice Models: A Semi-parametric Approach. Working
Paper No. E-180-95, The Center for Business and Economic Research,
College of Business and Economics, University of Kentucky.
(This paper was referenced by Dominitz, J. and R. P. Sherman (2005): Some Convergence Theory for Iterative
Estimation Procedures with an Application to
Semiparametric Estimation. Econometric Theory, 21, 838-863. Link1, Link2
And a formal complete proof of consistency for our estimator is given by Tanaka H. (2008) Link (this link no longer work). A newer version of this paper is
Tanaka, H. (2013). Local consistancy of the iterative least-squares estimator for semiparametric binary choice model. in Advances in Mathematical
Economics, 139-161, Springer Japan. and see also Tanaka, H. and Hoshino, T. (2011): Consistency of the Iterative Least Squares Estimator for the
Binary Choice Model with Varying Coefficients. Link2
Our paper is also discussed in the book Nonparametric Econometrics by Pagan and Ullah (Cambridge Univ. Press).
A recent (2021) paper related to Our Estimator is this: link
Some R code for computing the Wang-Zhou estimator is here and one more example here. C program written for Splus isot31.c and the Splus program to call it isot31.s
Pan and Zhou (1998)
Using 1-parameter sub-family of distributions
in empirical likelihood ratio with censored data
Updated 1/2001
Pan and Zhou (1998) Empirical
likelihood ratios in terms of cumulative hazard.
Zhou and Chen (1999) Testing and
confidece intervals with doubly censored dada.
Zhou (1999) Blinded Power estimation for the Kaplan-Meier/Nelson-Aalen.
(how to estimate power of a test when data are still blinded?)
Zhou (1999) Nonparametric Bayes estimator of Survival functions with
interval/doubly censored data. color PDF (The result concern limit of Bayes and NPMLE is interresting.)
Zhou (2000)
Empirical Envelope MLE and likelihood ratio test.
Zhou (2000)
Nonparametric Bayes estimator of survival functions
for doubly/interval censored data. Updated 2002.
Zhou (2000)
Understanding the Cox regression model with time-change covariates.
An updated version (include frailty models). (9/2001)
Chen and Zhou (2001)
Computing Censored Empirical likelihood by Quadratic Programing.
Zhou and Cui (2000) New Mathematical model for comparative judgment
Power
point file.
Presented at NIP 16 meeting in Vancouver.
Zhou, M. (2002)
Empirical
likelihood ratio for arbitrarily censored/truncated data by EM
algorithm.
Kim, K. and Zhou, M. (2003).
Symmetric location estimation/testing by empirical likelihood
Zhou, M. and Li, G. (2004).
Empirical likelihood analysis of the Buckley-James estimator
Zhou, M. (2004).
Empirical likelihood analysis of the rank estimator for the censored
AFT model.
Su, Y. and Zhou, M. (2004).
On a
connection between the Bradley-Terry model
and the Cox proportional hazards model.
Zhou, M. and Luan, J. (2005)
Nonparametric
Bayes Estimator of Survival Function for
Right-Censoring and Left-Truncation Data
Bathke, A., Kim, M. and Zhou, M. (2005)
Combine
multiple tests by empirical likelihood with censored data
Zhou, M. (2005)
The Cox
proportional hazards model with a partially known baseline
Zhou, M. Bathke, A., and Kim, M. (2007)
Empirical likelihood for Heteroscedastic AFT model.
Zhou, M. and Fang, H. (2006) A Comparison of Poisson and Bionomial
Empirical Likelihood.
Zhou, M. (2007) Empirical Likelihood for Counting Processes.
Zhou, M. and Jeong J. (2008) Empirical Likelihood Ratio Test for Mean and Median Residual Lifetime (with censored data)
Ren, J. and Zhou, M (2009) Full likelihood inference in the Cox model: An empirical likelihood approach. here
Zhou, M. (2009). A Wilks theorem for the censored empirical likelihood of Means (revised 2011)
Zhou, M., Kim, M., and Bathke, A. (2010) Empirical Likelihood Analysis for the Heteroscedastic Accelerated Failure Time Model.(update)
Kim, M. Zhou, M. and Jeong, J. (2012) Censored Quantile Regression for Residual Lifetimes. Lifetime Data Analysis
Zhou, M. and Yang, Y. (2013). A recursive algorithm for computing Kaplan-Meier under mean constrains 2013 version
Kim, M-O and Zhou, M. (2013). Size and shape of confidence regions from extended empirical likelihood tests. plot
Zhou, M. (2016). Empirical Likelihood Method in Survival Analysis A book published by CRC Press.
Kim, M-O and Zhou, M. (2019). Comparison of extended empirical likelihood methods: size and shape of test-based confidence regions.
Cui, Yifan; Zhu, Ruoqing; Zhou, Mai and Kosorok, Michael. (2020). Consistency of survival tree and forest models: splitting bias and correction (It contains a theorem
for the large sample property of the
Kaplan-Meier estimator when BOTH lifetimes AND censoring are non-identically distributed.)
Zhou, M. (2020). Restricted Mean Survival Time and Confidence Intervals by Empirical Likelihood Ratio (Appendix contains a proof of the empirical likelihood Wilks
theorem for right censored data.)
Zhou, M. (2020). A Note on the Computation of Empirical Likelihood Confidence Intervals. (Mean vs. hazard......Hazard confidence intervals are much faster to calculate).
Zhou, M. (2021). The Welch-Satterthwaite Adjustment for Censored Data Two-sample Restricted Mean Tests (Tech Report. It reduces type I error, among other things.)
Zhou, M. (2021). Semiparametric Observed Information For Kaplan-Meier Integrals and Nelson-Aalen Integrals. (Where a 1-parameter Least Favorable Family of distributions is identified).
Zhao, Y. Zhou, M. and Ding, X. (2022). Statistical Inference of AUC and pAUC by Empirical Likelihood. 5/2022 version The software used is now in an R package emplikAUC on CRAN, with some updates (Jan. 2023).
Some chinese short notes explaining statistics are on 'What's New' page.
Some R packages related to the research work:
(first two also available at CRAN)
emplik Empirical likelihood ratio, can handle censored/truncated
data. (it should be also on CRAN). A plot of
2-dim confidence region.
dblcens
Compute NPMLE of CDF from doubly censored data.
Now maintained by my former student Yifan Yang.
NPBayes
Nonparametric Bayes estimator of CDF from arbitrary censored data.
(link and package updated 6/2014)
rankreg: A package for rank estimators with censored AFT model.
CoxEL: A package to compute empirical likelihood test when side info
on baseline hazard is available for a Cox model.
emplik2:
A package I maintain, wrote by my former student (Barton)
for two sample censored data empirical likelihood ratio.
Ph.D. students I directed (with year graduated):
Ding, Li (1994); Zhang, Yuan (1995); Pan, XiaoRong (1997); Fang, Hui
(2000); Chen, Kun (2001);
Kim, Kyoungmi (2003);
Su, Yuhua (2003); Luan, Julia (2004);
Chen, Min (2005);
Zhu, Hua (2007); Huang, Liping (2009);
Barton, William (2010); Hu, Yanling (2011);
Zhang, Xiang (2013); Zhu, Shihong (2015); Shen, Zhiyuan (2015); Zhao, Yumin (2016); Yang, Yifan (2017); Ding, Xue (2020).
Slides of past presentations:
Log-rank test, improved.
PDF
file.
Empirical Likelihood and AFT models
PDF
file.
Computation of censored/truncated empirical likelihood ratio by EM
PDF file.
What is a Cox model?
Power
point file.
Improving Cox model.
PDF
file.
Power point file on the intro to empirical likelihood
Power point
file.
PDF file of 2 examples (simulations): double censored data and modified
Cox model estimators:
PDF file.