Related Research Articles
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.
Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.
Chemometrics is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as multivariate statistics, applied mathematics, and computer science, in order to address problems in chemistry, biochemistry, medicine, biology and chemical engineering. In this way, it mirrors other interdisciplinary fields, such as psychometrics and econometrics.
Herman Ole Andreas Wold was a Norwegian-born econometrician and statistician who had a long career in Sweden. Wold was known for his work in mathematical economics, in time series analysis, and in econometric statistics.
Decision tree learning is a supervised learning approach used in statistics, data mining and machine learning. In this formalism, a classification or regression decision tree is used as a predictive model to draw conclusions about a set of observations.
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory.
The Kruskal–Wallis test by ranks, Kruskal–Wallis test, or one-way ANOVA on ranks is a non-parametric statistical test for testing whether samples originate from the same distribution. It is used for comparing two or more independent samples of equal or different sample sizes. It extends the Mann–Whitney U test, which is used for comparing only two groups. The parametric equivalent of the Kruskal–Wallis test is the one-way analysis of variance (ANOVA).
When classification is performed by a computer, statistical methods are normally used to develop the algorithm.
The term kernel is used in statistical analysis to refer to a window function. The term "kernel" has several distinct meanings in different branches of statistics.
In statistics, multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables.
In statistics, multiple correspondence analysis (MCA) is a data analysis technique for nominal categorical data, used to detect and represent underlying structures in a data set. It does this by representing data as points in a low-dimensional Euclidean space. The procedure thus appears to be the counterpart of principal component analysis for categorical data. MCA can be viewed as an extension of simple correspondence analysis (CA) in that it is applicable to a large set of categorical variables.
In statistics, one purpose for the analysis of variance (ANOVA) is to analyze differences in means between groups. The test statistic, F, assumes independence of observations, homogeneous variances, and population normality. ANOVA on ranks is a statistic designed for situations when the normality assumption has been violated.
Peter J. Rousseeuw is a statistician known for his work on robust statistics and cluster analysis. He obtained his PhD in 1981 at the Vrije Universiteit Brussel, following research carried out at the ETH in Zurich, which led to a book on influence functions. Later he was professor at the Delft University of Technology, The Netherlands, at the University of Fribourg, Switzerland, and at the University of Antwerp, Belgium. Next he was a senior researcher at Renaissance Technologies. He then returned to Belgium as professor at KU Leuven, until becoming emeritus in 2022. His former PhD students include Annick Leroy, Hendrik Lopuhaä, Geert Molenberghs, Christophe Croux, Mia Hubert, Stefan Van Aelst, Tim Verdonck and Jakob Raymaekers.
In statistics, the two-way analysis of variance (ANOVA) is an extension of the one-way ANOVA that examines the influence of two different categorical independent variables on one continuous dependent variable. The two-way ANOVA not only aims at assessing the main effect of each independent variable but also if there is any interaction between them.
Log-linear analysis is a technique used in statistics to examine the relationship between more than two categorical variables. The technique is used for both hypothesis testing and model building. In both these uses, models are tested to find the most parsimonious model that best accounts for the variance in the observed frequencies.
In social sciences, sequence analysis (SA) is concerned with the analysis of sets of categorical sequences that typically describe longitudinal data. Analyzed sequences are encoded representations of, for example, individual life trajectories such as family formation, school to work transitions, working careers, but they may also describe daily or weekly time use or represent the evolution of observed or self-reported health, of political behaviors, or the development stages of organizations. Such sequences are chronologically ordered unlike words or DNA sequences for example.
The following outline is provided as an overview of, and topical guide to, machine learning:
The first edition of the textbook Data Science and Predictive Analytics: Biomedical and Health Applications using R, authored by Ivo D. Dinov, was published in August 2018 by Springer. The second edition of the book was printed in 2023.
In statistics, a sequence of random variables is homoscedastic if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The spellings homoskedasticity and heteroskedasticity are also frequently used. “Skedasticity” comes from the Ancient Greek word “skedánnymi”, meaning “to scatter”. Assuming a variable is homoscedastic when in reality it is heteroscedastic results in unbiased but inefficient point estimates and in biased estimates of standard errors, and may result in overestimating the goodness of fit as measured by the Pearson coefficient.
References
- 1 2 Ritschard, Gilbert (2013). "CHAID and Earlier Supervised Tree Methods". Contemporary Issues in Exploratory Data Mining in the Behavioral Sciences, McArdle, J.J. And G. Ritschard (Eds). New York: Routledge: 48–74.
- 1 2 Kass, G. V. (1980). "An Exploratory Technique for Investigating Large Quantities of Categorical Data". Applied Statistics. 29 (2): 119–127. doi:10.2307/2986296. JSTOR 2986296.
- 1 2 Biggs, David; De Ville, Barry; Suen, Ed (1991). "A method of choosing multiway partitions for classification and decision trees". Journal of Applied Statistics. 18 (1): 49–62. doi:10.1080/02664769100000005. ISSN 0266-4763.
- 1 2 Morgan, James N.; Sonquist, John A. (1963). "Problems in the Analysis of Survey Data, and a Proposal". Journal of the American Statistical Association. 58 (302): 415–434. doi:10.1080/01621459.1963.10500855. ISSN 0162-1459.
- 1 2 Messenger, Robert; Mandell, Lewis (1972). "A Modal Search Technique for Predictive Nominal Scale Multivariate Analysis". Journal of the American Statistical Association. 67 (340): 768–772. doi:10.1080/01621459.1972.10481290. ISSN 0162-1459.
- 1 2 Morgan, James N. (1973). THAID, a sequential analysis program for the analysis of nominal scale dependent variables. Robert C. Messenger. Ann Arbor, Mich. ISBN 0-87944-137-2. OCLC 666930.
{{cite book}}: CS1 maint: location missing publisher (link) - ↑ Belson, William A. (1959). "Matching and Prediction on the Principle of Biological Classification". Applied Statistics. 8 (2): 65–75. doi:10.2307/2985543. JSTOR 2985543.