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# Multivariate statistics

Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. [1]

66 relations: Admissible decision rule, Analysis of variance, Artificial neural network, Bayesian inference, Bayesian multivariate linear regression, Bias of an estimator, Canonical correlation, Canonical correspondence analysis, Cluster analysis, Correspondence analysis, Covariance mapping, Estimation of covariance matrices, EViews, Factor analysis, General linear model, Hotelling's T-squared distribution, Inverse-Wishart distribution, JMP (statistical software), Journal of the American Statistical Association, Likelihood-ratio test, Linear discriminant analysis, MATLAB, Minitab, Monotonic function, Multidimensional scaling, Multivariate analysis, Multivariate analysis of covariance, Multivariate analysis of variance, Multivariate normal distribution, Multivariate t-distribution, Multivariate testing, Normal distribution, OpenOffice.org, Parallel coordinates, Power (statistics), Principal component analysis, Principal response curve, Probability distribution, PSPP, Python (programming language), R (programming language), Recursive partitioning, Regression analysis, RV coefficient, SAS (software), SciPy, Simple linear regression, Simultaneous equations model, SmartPLS, SPSS, ... Expand index (16 more) »

In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is not any other rule that is always "better" than it (or at least sometimes better and never worse), in the precise sense of "better" defined below.

## Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample.

## Artificial neural network

Artificial neural networks (ANNs) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains.

## Bayesian inference

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.

## Bayesian multivariate linear regression

In statistics, Bayesian multivariate linear regression is a Bayesian approach to multivariate linear regression, i.e. linear regression where the predicted outcome is a vector of correlated random variables rather than a single scalar random variable.

## Bias of an estimator

In statistics, the bias (or bias function) of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated.

## Canonical correlation

In statistics, canonical-correlation analysis (CCA) is a way of inferring information from cross-covariance matrices.

## Canonical correspondence analysis

In applied statistics, canonical correspondence analysis (CCA) is a multivariate constrained ordination technique that extracts major gradients among combinations of explanatory variables in a dataset.

## Cluster analysis

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters).

## Correspondence analysis

Correspondence analysis (CA) or reciprocal averaging is a multivariate statistical technique proposed by Hirschfeld and later developed by Jean-Paul Benzécri.

## Covariance mapping

In statistics, covariance mapping is an extension of the covariance concept from random variables to random functions.

## Estimation of covariance matrices

In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated.

## EViews

EViews (Econometric Views) is a statistical package for Windows, used mainly for time-series oriented econometric analysis.

## Factor analysis

Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.

## General linear model

The general linear model or multivariate regression model is a statistical linear model.

## Hotelling's T-squared distribution

In statistics Hotelling's T-squared distribution (T2) is a multivariate distribution proportional to the ''F''-distribution and arises importantly as the distribution of a set of statistics which are natural generalizations of the statistics underlying Student's ''t''-distribution.

## Inverse-Wishart distribution

In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices.

## JMP (statistical software)

JMP (pronounced "jump") is a suite of computer programs for statistical analysis developed by the JMP business unit of SAS Institute.

## Journal of the American Statistical Association

The Journal of the American Statistical Association (JASA) is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States.

## Likelihood-ratio test

In statistics, a likelihood ratio test (LR test) is a statistical test used for comparing the goodness of fit of two statistical models — a null model against an alternative model.

## Linear discriminant analysis

Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events.

## MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.

## Minitab

Minitab is a statistics package developed at the Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr., and Brian L. Joiner in 1972.

## Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

## Multidimensional scaling

Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset.

## Multivariate analysis

Multivariate analysis (MVA) is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical outcome variable at a time.

## Multivariate analysis of covariance

Multivariate analysis of covariance (MANCOVA) is an extension of analysis of covariance (ANCOVA) methods to cover cases where there is more than one dependent variable and where the control of concomitant continuous independent variables – covariates – is required.

## Multivariate analysis of variance

In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means.

## Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions.

## Multivariate t-distribution

In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution.

## Multivariate testing

Multivariate testing is hypothesis testing in the context of multivariate statistics.

## Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

## OpenOffice.org

OpenOffice.org (OOo), commonly known as OpenOffice, is a discontinued open-source office suite.

## Parallel coordinates

Parallel coordinates are a common way of visualizing high-dimensional geometry and analyzing multivariate data.

## Power (statistics)

The power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis (H0) when a specific alternative hypothesis (H1) is true.

## Principal component analysis

Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.

## Principal response curve

In multivariate statistics, principal response curves (PRC) are used for analysis of treatment effects in experiments with a repeated measures design.

## Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

## PSPP

PSPP is a free software application for analysis of sampled data, intended as a free alternative for IBM SPSS Statistics.

## Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

## R (programming language)

R is a programming language and free software environment for statistical computing and graphics that is supported by the R Foundation for Statistical Computing.

## Recursive partitioning

Recursive partitioning is a statistical method for multivariable analysis.

## Regression analysis

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables.

## RV coefficient

In statistics, the RV coefficient is a multivariate generalization of the squared Pearson correlation coefficient (because the RV coefficient takes values between 0 and 1).

## SAS (software)

SAS (previously "Statistical Analysis System") is a software suite developed by SAS Institute for advanced analytics, multivariate analyses, business intelligence, data management, and predictive analytics.

## SciPy

SciPy (pronounced /ˈsaɪpaɪ'/ "Sigh Pie") is a free and open-source Python library used for scientific computing and technical computing.

## Simple linear regression

In statistics, simple linear regression is a linear regression model with a single explanatory variable.

## Simultaneous equations model

Simultaneous equation models are a type of statistical model in the form of a set of linear simultaneous equations.

## SmartPLS

SmartPLS is a software with graphical user interface for variance-based structural equation modeling (SEM) using the partial least squares (PLS) path modeling method.

## SPSS

SPSS Statistics is a software package used for interactive, or batched, statistical analysis.

## Stata

Stata is a general-purpose statistical software package created in 1985 by StataCorp.

## Statistica

Statistica is an advanced analytics software package originally developed by StatSoft which was acquired by Dell in March 2014.

## Statistical graphics

Statistical graphics, also known as graphical techniques, are graphics in the field of statistics used to visualize quantitative data.

## Statistical hypothesis testing

A statistical hypothesis, sometimes called confirmatory data analysis, is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.

## Statistical inference

Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution.

## Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

## Structural equation modeling

Structural equation modeling (SEM) includes a diverse set of mathematical models, computer algorithms, and statistical methods that fit networks of constructs to data.

## Structured data analysis (statistics)

Structured data analysis is the statistical data analysis of structured data.

## Student's t-distribution

In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

## The Unscrambler

The Unscrambler® X is a commercial software product for multivariate data analysis, used for calibration of multivariate data which is often in the application of analytical data such as near infrared spectroscopy and Raman spectroscopy, and development of predictive models for use in real-time spectroscopic analysis of materials.

## Theodore Wilbur Anderson

Theodore Wilbur Anderson (June 5, 1918 &ndash; September 17, 2016) was an American mathematician and statistician who has specialized in the analysis of multivariate data.

## Time series

A time series is a series of data points indexed (or listed or graphed) in time order.

## Univariate analysis

Univariate analysis is perhaps the simplest form of statistical analysis.

## Vector autoregression

Vector autoregression (VAR) is a stochastic process model used to capture the linear interdependencies among multiple time series.

## WarpPLS

WarpPLS is a software with graphical user interface for variance-based and factor-based structural equation modeling (SEM) using the partial least squares and factor-based methods.

## Wishart distribution

In statistics, the Wishart distribution is a generalization to multiple dimensions of the chi-squared distribution, or, in the case of non-integer degrees of freedom, of the gamma distribution.

## References

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