About Me

Institute of Statistical Science Academia Sinica
Taipei 11529, Taiwan, R.O.C.
Tel : 886-2-27835611 ext. 212
FAX : 886-2-27831523
Research Interests

‧Categorical Data Analysis
‧Educational Statistics
‧Missing Data Analysis
‧Nonparametric Regression
‧Statistics for Brain fMRI (functional Magnetic Resonance Imaging)


1980 PhD, Florida state University, U.S.A.

Professional Experience

1987 – present Research Fellow, Institute of Statistical Science, Academia Sinica

1983 – 1987 Associate Research Fellow, Institute of Statistical Science, Academia Sinica

1980 – 1983 Assistant Professor, Department of Mathematics, University of Houston

Research Findings (since 2010)
  • Likelihood Ratio Tests with Three-Way Tables (2010 JASA, 740-749): The Mantel–Haenszel test (1959, J. Nat. Cancer Inst.) is often found overly sensitive. Based on the Pythagorean law of relative entropy, a two-step likelihood ratio test is developed to give proper p-values in testing for both 3-way interaction and partial association between two variables given the remaining variables. This law extends to giving the desired information identity of discrete multivariate data such that proper main and interaction effects are constructed for use with a generalized linear model.
  • On Hyperbolic Transformations to Normality (2017 CSDA, 250-266): A new family of hyperbolic power transformations is shown to outperform the existing families in achieving higher accuracy of testing goodness-of-fit to normality for general data distributions. In particular, it is capable of transforming bimodal data distributions to normality. On the Behrens-Fisher problem, the Welch t-test is known to be robust against mild skewness and unequal variances, but the proposed transformations show that it can be non-robust against violation of normality in the kurtosis, other than complicate skewness in the data distribution.
  • Convex Mixtures Imputation and Applications (Statistica Sinica, to appear 2018-19): Since 1951, the k-nearest neighbor density/regression estimation rules have been widely used in the literature of engineering science and machine learning; and kernel density/regression estimation rules have also been popular in the statistical science. A collaboration of these two principle methods is for the first time employed in the assessment of nonparametric imputation with missing data. It is initially found that the crucial necessary condition, the probability of observing the target variable be positive and bounded above zero in the domain of the covariates, can be relaxed by using convex mixtures of these two imputation rules. This improves the accuracy in both estimation and unsupervised prediction over the existing methods when the incomplete data distributions are not ideally regular in general applications.
  • A Constructive Procedure for Modeling Categorical Variables: Log-linear and Logit Models (rejected by Statistical Methods in Medical Research “no review comments”, December 27, 2017; coauthors M. Liou, J.W. Liou and H.W. Kao). Abstract: Association of discrete multivariate data is analyzed using the information identities based on multivariate multinomial distributions. A geometric decomposition of information identity is developed to identify the useful predictors and interaction effects to be used in a generalized linear model. As a new approach to constructing concise (parsimonious) log-linear and logit models, it facilitates the search for less parsimonious AIC models as a byproduct. In general, the method directly yields needed main and interaction effects before choosing a non-normal regression model for moderately large parameters and large data, which is not achieved with BIC.
Selected Publications

[R4]    P.C. Kuo, Y.L. Tseng, K. Zilles, S. Suen, S.B. Eickhoff, J.D. Lee, P.E. Cheng, M. Liou. Brain Dynamics and Connectivity Networks under Natural Auditory Stimulation. NeuroImage, 202 (2019), 116042.

[R3]    J. Ning, M. Liou, P.E. Cheng. Convex Mixtures Imputation and Applications. Statistica Sinica, 29 (2019), 329-351.

[R2]    J.W. Liou, P.E. Cheng, H.W. Kao, M. Liou. Construction of Log-linear and Logit Models via Mutual Information Identity. arXiv 1801.01278 [stat.ME] (2018).

[R1]    A.C. Tsai, M. Liou, M. Simak, P.E. Cheng. On hyperbolic transformations to normality. Computational Statistics and Data Analysis, 115, (2017) 250-266.

[1] P.E.Cheng and G.D.Lin. Maximum Likelihood Estimation of a Survival Function under the Koziol-Green Proportional Hazards Model. Statistics and Probability Letters, 5, (1987), 75-80.

[2] P.E. Cheng. Nonparametric Estimation of Mean Functionals with Data Missing at Random. Journal of the American Statistical Association, 89 (1994), 81-87.

[3] P.E. Cheng and M. Liou. Computerized Adaptive Testing Using the Nearest-Neighbors Criterion. Applied Psychological Measurement, 27 (2003), 204-216.

[4] P.E. Cheng, M. Liou, J.A.D. Aston and A. Tsai. Information Identities and Testing Hypotheses: Power Analysis for Contingency Tables. (2005, ISS TR 2005-02, in press, Statistica Sinica, 2008)

[5] P.E. Cheng, J.W. Liou, M. Liou and J.A.D. Aston. Data Information in Contingency Tables: A Fallacy of Hierarchical Log-linear Models. Journal of Data Science, 4 (2006), 387-398.

[6] P.E. Cheng, J.W. Liou, M. Liou and J.A.D. Aston. Linear Information Models: An Introduction. Journal of Data Science, 5 (2007), 297-314.

[7] P.E. Cheng, M. Liou and J.A.D. Aston. Likelihood Ratio Tests with Three-Way Tables. (2007, ISS TR 2007-03; in presss, JASA).

[8] Li-De Ho and P.E. Cheng. Testing Generalized Lorenz Dominance (1998). Thesis, National Donghwa University.

[9] Lee, J.D., Su, H.R., Cheng, P.E., Liou, M., Aston, J., Tsai, A.C. and C.Y. Chen. MR Image Segmentation using a Power Transformation Approach. (2005); IEEE Transactions on Medical Imaging,28,(2009),894-905.

[10] P.E. Cheng, J.W. Liou, M. Liou and J.A.D. Aston. Linear Information Models : A Revisit. (2009, ISS TR 2009-01).

[11] A Comparision Study of Nonparametric Imputation Methods, revised July, 2010. J.H. Ning and P.E. Cheng.