Institute of Statistical Science

In July 1980, while attending the 14th assembly of members of Academia Sinica, a group of twenty-one members, including Professors C. C. Li, Y. S. Chow and G. C. Tiao, drafted a resolution calling for the establishment of theInstitute of Statistics. Later, the Council of Academia Sinica confirmed the resolution and recommended establishing a preparatory office. The approval was granted by the President of the Republic of China in February 1981. An advisory board composed of thirteen was soon formed: Prof. Y. S. Chow served as the chairman of the board, and Dr. M. T. Chao was appointed the director of the preparatory office. On July 1, 1982, the preparatory office was officially founded.

The advisory board recommended removing the status of preparatory office in 1987. The recommendation was approved on August 3, 1987 by the Presidential Office. At the same time, the name of this institute was changed to the "Institute of Statistical Science" and Dr. M. T. Chao took the first and second directorship. In August 1993, Dr. C. Z. Wei succeeded Dr. Chao as the director, and Dr. G. D. Lin was appointed the deputy director.

RESEARCH

MATHEMATICAL STATISTICS

• Survival and related statistical methods
• Bootstraps
• Characterization of distributions
• Ranking and selection methods
• Nonparametric regression, density and hazard rate function estimation
• Studies of incomplete data
• Stochastic regression analysis
• Mixture distributions
• Sequential methods
• Time series and long range dependent process
• Classical probability problems
• Estimations in change-point model
• M-estimation in robust statistics
• Experimental design
• Bayesian analysis
• Studies of directional data
• Decision theory
• Limit theorems for arithmetic functions and combinatorial structures

BIOSTATISTICS

• Statistical genetics
• Theoretical study of image processing when applied to medical studies
• Cooperative cancer clinical trial studies

INDUSTRIAL STATISTICS

• Promotion of the concept of statistical technology and development of related techniques for quality and productivity improvement

SOCIOLOGICAL STATISTICS

• Statistical evaluation of achievement tests
• Large scale analysis of college entrance examination data in Taiwan

STATISTICAL COMPUTING AND GRAPHICS

• High-dimensional data visualization
• Dynamic graphical model diagnostic
• Graphics linkage method

PERSONNEL AND FACILITIES

PERSONNEL

The staff consists of 13 research fellows, 8 associate research fellows, 10 assistant research fellows, 2 post-doctoral fellows, 1 technician and 6 administrative personnel.

Computer Room

COMPUTER ROOM

• Hardware:
  IBM 590

  1
  IBM 25T W/S	6
  IBM 41T W/S	1
  IBM 3BT File Server	1
  IBM M20 W/S	1
  SUN SPARC M20 W/S	1
  HP 720 W/S	1
  PC	9
  MAC	3
  Laser Printers	6
  HP 7550A Plotter	1

• Software:
  E-mail System (TANET, INTERNET)
  SAS
  S-PLUS
  SCA
  FORTRAN 77
  FORTRAN 90
  TEX/LATEX
  C Compiler
  CIS
  Gauss
  Mathematica
  Xlispstat
  Softwares for PC & Mac
  
• Network:
  All machines are networked. Through the Netware, Lansmart and TCP/IP, our PCs, Macs and workstations can share all the resources in the Institute. This network system is also connected to the campus-wide FDDI network.

Library

LIBRARY

MAJOR RESULTS OF RESEARCH

MATHEMATICAL STATISTICS

• A sufficient condition for the weak convergence of a recursion is established.
• Using a regression type density estimator, the boundary problem encountered in the kernel estimators has been resolved.
• A stochastic Peter principle was proposed to interpret the abundance model.
• e-admissibility and 0⁺-admissibility. In these joint results, two sufficient conditions were obtained for e-admissibility and one sufficient condition was derived for 0⁺-admissibility. Three examples were illustrated.
• Testing and estimations in the linear error-in-variables models with change-point. A likelihood ratio test was proposed for the test of no change against exactly one change. Estimators for change-point and some other related parameters were proposed and its limiting behaviors have been studied. Two sets of real data were also analyzed.
• Resolve a basic problem for twenty-five years on nonparametric regression strong convergence rates from the infinite-variance viewpoint. Indeed, it is based on a similar extension to the Hardy-Littlewood (1914) strong law.
• Prove a Paley-type inequality related to CLT for Markov chains, which generalizes that of i.i.d. case given by Y. S. Chow.
• Find a corrected normal approximation and large devi-ations approximation, in ruin probability for Markov random walks.
• Accomplish approximation to the variance of the first passage time for Markov random walks.
• Importance resampling and related probability problems for Markov chains.
• Investigate the problem of how to compare the relative importance of components in a given coherent system when the component reliabilities are unknown. We also introduced several different measures of component importance.
• Provide several criteria for the problem of where to allocate redundancy components to a system in order to maximize the system reliability.
• Obtain consistent estimators for polynomial measurement error model, which is an important case of general nonlinear measurement error models. The resulting estimators are simple, explicit and easy to compute. We also made some corrections to the existing results (JRSSB, 1985 pp. 510-518) and made a more precise analysis toward the model structure as well.
• Establish the strong consistency of a sequential pro-cedure for estimation in the quasi-likelihood using the last-time technique.
• Introduce a new method of sampling-- refined composite sampling. The method can be applied to monitoring in environmental engineering. Besides helping save a lot of analysis costs, it also has good "effectiveness" and "efficiency".
• In the ongoing project, "Measuring top-down correlation", important weighted rank correlation coeffic-ients were proposed and studied. The measures can be applied to sensitivity analysis, library sciences, and marketing, among others.
• Propose a class of confidence sets for the bioequi-valence testing problem. The proposed sets were shown to have the shortest expected effective length at the origin; hence they proved to be better, more powerful, bioequivalence tests.
• In stratification sampling problems, the number of strata is huge, while the sample size within each stratum is small. This is called the small area estimation problem. In this situation, there seems to be a need to design confidence set procedures that "borrow strength" from other populations. We proposed a class of confidence sets and showed them to be better than the classical region in the small area estimation problem.
• Investigate limit theorems for arithmetic functions and combinatorial structures. Many related analytic tech-niques can also be applied to probability distributions.
• Derive asymptotic normality for five random variables defined on random permutation by martingale central limit theorem.
• An error bound in the normal approximation to the distribution of the double-indexed permutation statistics S_i,ja(i, j, p(i), p(j) ) was derived based on Stein's method and Bolthausen's combinatorial methods.
• Let X=(X₁, ..., X_p)' be a p-dimensional normal random vetor with mean q=(q₁, ...,q_p )' and identity as the covariance matrix. For the problem of estimating the mean parameters q₁, ...,q_p simultaneously under the squared error loss, we studied lots of estimators which improve upon the usual MLE X=(X₁, ..., X_p)' and considered the performance of the saving risk of these improved estimators over the usual X. We found that:
  1) As q=(q₁, ...,q_p )' is away from 0, the improving percentage, (the saving risk /p)*100, of James-Stein estimator or the modified one drops down to 0 dramatically.
  2) For any given constant C, the Hudson improved estimator or the modified one has the "Robust" improving percentage for any
  qÎ{q: S_i=1,...,p(q_i - \bar(q))²£C}, \bar(q)=S_i=1,...,p(1/p)*q_i .

Publications

BIOSTATISTICS

• Efficient estimators have been obtained for various generalized Cox regression models and the results can be applied to recurrent event data analysis.
• The maximum likelihood estimator for positron emi-ssion tomography was studied by sieve method. This method suggests that the number of pixels need to be in line with the number of detectors in order to avoid poor image reconstruction.
• An efficient estimator is obtained for a time-dependent frailty model and the results can be applied to survival data analysis with random clusters.
• Semi-parametric counting process approach was pro-posed to study the estimation of treatment effect under biased allocation.
• Optimal nonparametric tests were obtained for K-sample frailty models.
• Propose a two-stage method to detect pseudo-random mating populations and to calculate the probability of correct determination.
• Propose a statistical procedure for confirmation analysis.
• Discuss the statistical properties of the self-contained subset method.
• Use multivariate statistical method to analyze hospital accreditation data.
• Perform a Chinese population study of Apo B gene for cardiovascular diseases.
• An extension of the mixture regression model in event history analysis with nonsusceptible fraction to dealing with the data with general censorships.
• In a collaborative project of schizophrenia study, a computerized data management system has been implemented, and statistical methods in event history analysis and clustering analysis have been investigated.

SOCIOLOGICAL STATISTICS

• Research on multivariate imputation methods for ana-lyzing data that are collected from a balanced incomplete data design of large scale assessments and lengthy questioners.
• Investigate the consequence of assuming ignorable and nonignorable models on equipercentile equating.
• Investigate the incomplete block designs for collecting data for the Social Change Survey in Taiwan.

STATISTICAL COMPUTING AND GRAPHICS

• Develop an interactive diagnostic system for graphically diagnosing multidimensional scaling related models.
• Develop a dynamic graphic environment, generalized association plot (GAP), for visualizing proximity among a group of variables or subjects and associations between variables and subjects.
• Discover the convergence and convergent properties of iterated formed series of Pearson product moment correlation matrices. Apply the elliptical structure of converging correlation matrices to improve the solutions to the following problems:
  1) Binary-splitting a set of objects into two disjointed groups.
  2) Use this splitting rule to develop a new type of divisive cluster tree.
  3) The seriation problem.

Discussion Room

EXPERIMENTAL DESIGNS

• The existence of the balanced generalized two-way designs was shown by a simple constructive proof.
• The Yeh-Bradley conjecture was further studied. More designs were shown to confirm this conjecture.
• The necessary and sufficient conditions for the OMEP were studied. These conditions were also used to construct the minimal OMEP.

ENVIRONMENTAL STATISTICS

An improved method for receptor model was proposed which is useful for validating source inventory and managing air quality in metropolitan areas.

RESEARCH STAFF

MEMBER OF THE ADVISORY COMMITTEE