Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.
In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in
Calyampudi Radhakrishna Rao,, commonly known as C. R. Rao, is an Indian-American mathematician and statistician. He is currently professor emeritus at Pennsylvania State University and Research Professor at the University at Buffalo. Rao has been honoured by numerous colloquia, honorary degrees, and festschrifts and was awarded the US National Medal of Science in 2002. The American Statistical Association has described him as "a living legend whose work has influenced not just statistics, but has had far reaching implications for fields as varied as economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine." The Times of India listed Rao as one of the top 10 Indian scientists of all time. In 2023, Rao was awarded the International Prize in Statistics, an award often touted as the "statistics’ equivalent of the Nobel Prize". Rao is also a Senior Policy and Statistics advisor for the Indian Heart Association non-profit focused on raising South Asian cardiovascular disease awareness.
Directional statistics is the subdiscipline of statistics that deals with directions, axes or rotations in Rn. More generally, directional statistics deals with observations on compact Riemannian manifolds including the Stiefel manifold.
Warren John Ewens is an Australian-born mathematician who has been Professor of Biology at the University of Pennsylvania since 1997. He concentrates his research on the mathematical, statistical and theoretical aspects of population genetics. Ewens has worked in mathematical population genetics, computational biology, and evolutionary population genetics. He introduced Ewens's sampling formula.
Samarendra Nath Roy was an Indian-born American mathematician and an applied statistician.
Hirotsugu Akaike was a Japanese statistician. In the early 1970s, he formulated the Akaike information criterion (AIC). AIC is now widely used for model selection, which is commonly the most difficult aspect of statistical inference; additionally, AIC is the basis of a paradigm for the foundations of statistics. Akaike also made major contributions to the study of time series. As well, he had a large role in the general development of statistics in Japan.
In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.
In statistics, the term higher-order statistics (HOS) refers to functions which use the third or higher power of a sample, as opposed to more conventional techniques of lower-order statistics, which use constant, linear, and quadratic terms. The third and higher moments, as used in the skewness and kurtosis, are examples of HOS, whereas the first and second moments, as used in the arithmetic mean (first), and variance (second) are examples of low-order statistics. HOS are particularly used in the estimation of shape parameters, such as skewness and kurtosis, as when measuring the deviation of a distribution from the normal distribution.
Karl Gustav Jöreskog is a Swedish statistician. Jöreskog is a professor emeritus at Uppsala University, and a co-author of the LISREL statistical program. He is also a member of the Royal Swedish Academy of Sciences. Jöreskog received his bachelor's, master's, and doctoral degrees at Uppsala University. He is also a former student of Herman Wold. He was a statistician at Educational Testing Service (ETS) and a visiting professor at Princeton University.
Theodore Wilbur Anderson was an American mathematician and statistician who specialized in the analysis of multivariate data. He was born in Minneapolis, Minnesota. He was on the faculty of Columbia University from 1946 until moving to Stanford University in 1967, becoming Emeritus Professor in 1988. He served as Editor of Annals of Mathematical Statistics from 1950 to 1952. He was elected President of the Institute of Mathematical Statistics in 1962.
In statistics, L-moments are a sequence of statistics used to summarize the shape of a probability distribution. They are linear combinations of order statistics (L-statistics) analogous to conventional moments, and can be used to calculate quantities analogous to standard deviation, skewness and kurtosis, termed the L-scale, L-skewness and L-kurtosis respectively. Standardised L-moments are called L-moment ratios and are analogous to standardized moments. Just as for conventional moments, a theoretical distribution has a set of population L-moments. Sample L-moments can be defined for a sample from the population, and can be used as estimators of the population L-moments.
Ramanathan Gnanadesikan was an Indian statistician, known for his work in multivariate data analysis and leadership in the field. He received his Ph.D. at the University of North Carolina and headed research groups in statistics at Bell Laboratories and Bellcore. He was a fellow of American Association for the Advancement of Science, American Statistical Association, Institute of Mathematical Statistics and Royal Statistical Society, and elected member of the International Statistical Institute. He served as President of Institute of Mathematical Statistics and the International Association for Statistical Computing, the latter of which he helped found.
Robert Tibshirani is a professor in the Departments of Statistics and Biomedical Data Science at Stanford University. He was a professor at the University of Toronto from 1985 to 1998. In his work, he develops statistical tools for the analysis of complex datasets, most recently in genomics and proteomics.
Trevor John Hastie is an American statistician and computer scientist. He is currently serving as the John A. Overdeck Professor of Mathematical Sciences and Professor of Statistics at Stanford University. Hastie is known for his contributions to applied statistics, especially in the field of machine learning, data mining, and bioinformatics. He has authored several popular books in statistical learning, including The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Hastie has been listed as an ISI Highly Cited Author in Mathematics by the ISI Web of Knowledge.
Bani K. Mallick is a Distinguished Professor and Susan M. Arseven `75 Chair in Data Science and Computational Statistics in the Department of Statistics at Texas A&M University in College Station. He is the Director of the Center for Statistical Bioinformatics. Mallick is well known for his contribution to the theory and practice of Bayesian semiparametric methods and uncertainty quantification. Mallick is an elected fellow of American Association for the Advancement of Science, American Statistical Association, Institute of Mathematical Statistics, International Statistical Institute and the Royal Statistical Society. He received the Distinguished research award from Texas A&M University and the Young Researcher award from the International Indian Statistical Association.
Fang Kaitai, also known as Kai-Tai Fang, is a Chinese mathematician and statistician who has helped to develop generalized multivariate analysis, which extends classical multivariate analysis beyond the multivariate normal distribution to more general elliptical distributions. He has also contributed to the design of experiments.
Narayanaswamy Srinivasan was an Indian molecular biophysicist and a professor and the head of Proteins: Structure, Function and Evolutionary Group at the Molecular Biophysics Unit of the Indian Institute of Science. He is known for his researches in the fields of computational genomics and protein structure analysis. An elected fellow of the Indian Academy of Sciences and the National Academy of Sciences, India, he is a J. C. Bose National fellow of the Department of Biotechnology and a recipient of the National Bioscience Award for Career Development of the Department of Science and Technology. The Council of Scientific and Industrial Research, the apex agency of the Government of India for scientific research, awarded him the Shanti Swarup Bhatnagar Prize for Science and Technology, one of the highest Indian science awards, in 2007, for his contributions to biological sciences.
Geoffrey John McLachlan FAA is an Australian researcher in computational statistics, machine learning and pattern recognition. McLachlan is best known for his work in classification and finite mixture models. He is the joint author of five influential books on the topics of mixtures and classification, as well as their applications. Currently, McLachlan is a Professor of statistics within the School of Mathematics and Physics at the University of Queensland.
Dipak Kumar Dey is an Indian-American statistician best known for his work on Bayesian methodologies. He is currently the Board of Trustees Distinguished Professor in the Department of Statistics at the University of Connecticut. Dey has an international reputation as a statistician as well as a data scientist. Since he earned a Ph.D. degree in statistics from Purdue University in 1980, Dey has made tremendous contributions to the development of modern statistics, especially in Bayesian analysis, decision science and model selection. Dey has published more than 10 books and edited volumes, and over 260 research articles in peer-refereed national and international journals. In addition, the statistical methodologies that he has developed has found wide applications in a plethora of interdisciplinary and applied fields, such as biometry and bioinformatics, genetics, econometrics, environmental science, and social science. Dey has supervised 40 Ph.D. students, and presented more than 200 professional talks in colloquia, seminars and conferences all over the world. During his career, Dey has been a visiting professor or scholar at many institutions or research centers around the world, such as Macquarie University, Pontificia Universidad Católica de Chile,, University of São Paulo, University of British Columbia, Statistical and Applied Mathematical Sciences Institute, etc. Dey is an elected fellow of the American Association for the Advancement of Science, the American Statistical Association, the Institute of Mathematical Statistics, the International Society for Bayesian Analysis and the International Statistical Institute.
