Fang Kaitai (; born 1940), also known as Kai-Tai Fang, is a Chinese mathematician and statistician who has helped to develop generalized
multivariate analysis
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.
Multivariate statistics concerns understanding the different aims and background of each of the dif ...
, which extends classical multivariate analysis beyond the
multivariate normal distribution to more general
elliptical distribution
In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint di ...
s.
He has also contributed to the
design of experiments
The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...
.
Selected university offices and honors
Fang is Director of Institute of Statistics and Computational Intelligence and Emeritus Professor at
Hong Kong Baptist University
Hong Kong Baptist University (HKBU) is a publicly funded tertiary liberal arts education, liberal arts institution with a Christian ethics, Christian education heritage. It was established as Hong Kong Baptist College with the support of Ame ...
,
after having been Full Professor of the Institute of Applied Mathematics of the
Chinese Academy of Sciences.
He is an Elected Fellow (or Elected Member) of the
Institute of Mathematical Statistics
The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts o ...
,
of the
International Statistical Institute
The International Statistical Institute (ISI) is a professional association of statisticians. It was founded in 1885, although there had been international statistical congresses since 1853. The institute has about 4,000 elected members from gov ...
(ISI), of the
American Statistical Association (ASA), and of the Hong Kong Statistical Society (HKSS).
[Homepage](_blank)
at Hong Kong Baptist University.[200]
Fellows of the American Statistical Association (ASA)
, accessed 2016-09-02. The Hong Kong Baptist University honored Professor Fang with the President's Award for Outstanding Performance in Scholarly Work in 2001.
Fang and Zhang's book ''Generalized multivariate analysis'' was honored as a "most excellent book in China"
[Loie describes the award as only "most excellent book", without the ]indefinite article
An article is any member of a class of dedicated words that are used with noun phrases to mark the identifiability of the referents of the noun phrases. The category of articles constitutes a part of speech.
In English, both "the" and "a(n)" ar ...
"a", which here is inserted (in accordance with standard written English
English orthography is the writing system used to represent spoken English, allowing readers to connect the graphemes to sound and to meaning. It includes English's norms of spelling, hyphenation, capitalisation, word breaks, emphasis, and p ...
). by the Government Information and Publication Administration.
Biography
Fang's early life is described by Agnes Loie in a volume published on his 65th birthday.
Fang was born in 1940 in
Taizhou in the province of
Jiangsu
Jiangsu (; ; pinyin: Jiāngsū, Postal romanization, alternatively romanized as Kiangsu or Chiangsu) is an Eastern China, eastern coastal Provinces of the People's Republic of China, province of the China, People's Republic of China. It is o ...
in China. He graduated from Jiangsu's
Yangzhou High School
Yangzhou High School of Jiangsu Province () is a high school in Yangzhou, Jiangsu, China. It grew out of Yidong School, which was established in 1902.
Overview
Yangzhou High school, one of the key and model schools in Jiangsu Province, is among ...
.
University studies and the Cultural Revolution
In 1957 he studied mathematics at
Peking University
Peking University (PKU; ) is a public research university in Beijing, China. The university is funded by the Ministry of Education.
Peking University was established as the Imperial University of Peking in 1898 when it received its royal charter ...
, after which he entered the graduate program at the Institute of Mathematics of the
Chinese Academy of Sciences, in Beijing.
His doctoral supervisor was
Pao-Lu Hsu
Pao-Lu Hsu or Xu Baolu (; September 1, 1910 – December 18, 1970) was a Chinese mathematician noted for his work in probability theory and statistics.
Life and career
Pao-Lu Hsu was born in Beijing on September 1, 1910, with his ancestral hom ...
, who suggested that Fang provide a multivariate generalization and correction of a univariate result, which had been given an incomplete proof in a Russian paper. With two weeks' work, Fang's submitted his extensions, which were declared by Hsu to suffice for his dissertation. Unfortunately, this paper remained unpublished for 19 years because the Cultural Revolution destroyed academic publishing in China.
[According to , Fang's thesis was published as (with details from zbMath):
] Fang reported that his studies were halted for the ten years of the Cultural Revolution,
which lasted from 1966 to 1976.
After graduating from Peking University, he undertook postgraduate studies at the Institute of Mathematics of Academia Sinica, which had less "political chaos" than Peking University, according to Fang.
There, as a postgraduate researcher, Fang was supervised by Minyi Yue. In 1965, he was assigned to the
Anshan Steel and Iron Company, where he gave lectures to engineers and worked on
nonlinear regression
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fit ...
, before being sent to a rural village to work as a laborer for the rest of 1965 and 1966.
In 1972 Fang and other staff at the Academy of Sciences promoted the use of
experimental design
The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...
to improve
Tsingtao Beer
Tsingtao Brewery Co. Ltd. () is China's second largest brewery, with about 15% of domestic market share and also accounts for half of China’s national beer exports. It was founded in 1903 by German settlers in Tsingtau ( Qingdao), Kiautschou ...
.
Revival of academic life
Fang was successively appointed to be assistant researcher and assistant professor in 1978.
He then joined the Institute of Applied Mathematics of the Chinese Academy of Sciences, and he became Associate Professor in 1980 and associate director of the institute in 1984. He was appointed full professor in 1986.
Multivariate analysis

In mathematical statistics, Fang has published textbooks and monographs in
multivariate analysis
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.
Multivariate statistics concerns understanding the different aims and background of each of the dif ...
. In particular, his books have extended classical multivariate analysis beyond the
multivariate normal distribution to a
generalized multivariate analysis using more general ''
elliptical distribution
In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint di ...
s'', which have elliptically contoured distributions.
His book on ''Generalized multivariate analysis'' (with Zhang) has extensive results on multivariate analysis for elliptical distributions,
to which
T. W. Anderson refers readers of his ''An introduction to multivariate statistical analysis'' (3rd ed., 2003). The Fang and Zhang monograph used
matrix differential calculus.
One of ''Generalized multivariate analysiss innovations was its extensive use of the
multilinear algebra, particularly of the
Kronecker product
In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a generalization of the outer product (which is denoted by the same symbol) from vectors to ...
and of
vectorization, according to Kollo and von Rosen. Fang and Zhang's ''Generalized multivariate analysis'' was honored as a "most excellent book in China"
by the Government Information and Publication Administration.
Combinatorial design and experiments: uniform designs
Fang also has conducted research in the
design of experiments
The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...
. In 1972, he worked with the
Tsingdao Beer factory and other factories. He and other mathematical statisticians at the Chinese Academy of Sciences promoted the industrial use of orthogonal designs.
Orthogonal designs are discussed in the books and papers of Fang on "uniform designs" and also by other authors.
Fang recognized that high-dimensional
combinatorial designs, which had been used for
numerical integration
In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations ...
on the
unit cube by
Hua Luogeng and
Wang Yuan, could be used to study
interaction
Interaction is action that occurs between two or more objects, with broad use in philosophy and the sciences. It may refer to:
Science
* Interaction hypothesis, a theory of second language acquisition
* Interaction (statistics)
* Interactions o ...
, for example, in
factorial experiments and
response surface methodology
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM ...
. Collaborating with Wang led to Fang's uniform designs, which have been used also in
computer simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...
s.
References
*
*
*
Further reading
*
* A collection of tributes by
T. W. Anderson, Fred Hickerenell,
Rahul Mukerjee, Dietrich von Rosen,
Yuan Wang
The Yuan Wang-class of tracking ships () are used for tracking and support of satellite and intercontinental ballistic missiles by the People's Liberation Army Strategic Support Force of the People's Republic of China (PRC). It is important to no ...
, and Peter Winker.
External links
Homepage of Professor Fangat Hong Kong Baptist University
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*
*
*
{{DEFAULTSORT:Fang, Kaitai
1940 births
Living people
20th-century Chinese mathematicians
21st-century Chinese mathematicians
Chinese statisticians
Educators from Taizhou, Jiangsu
Elected Members of the International Statistical Institute
Fellows of the American Statistical Association
Fellows of the Institute of Mathematical Statistics
Academic staff of Hong Kong Baptist University
Mathematicians from Jiangsu
Peking University alumni
Scientists from Taizhou, Jiangsu