In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe the center of the income distribution because increases in the largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics.
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.
The following outline is provided as an overview of and topical guide to statistics:
In statistics, the Behrens–Fisher problem, named after Walter-Ulrich Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples.
Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. In the context of machine learning and more generally statistical analysis, this may be the selection of a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection. Given candidate models of similar predictive or explanatory power, the simplest model is most likely to be the best choice.
In probability theory, an empirical process is a stochastic process that characterizes the deviation of the empirical distribution function its expectation. In mean field theory, limit theorems are considered and generalise the central limit theorem for empirical measures. Applications of the theory of empirical processes arise in non-parametric statistics.
Richard David Gill is a British-Dutch mathematician. He has held academic positions in the Netherlands. As a probability theorist and statistician, Gill has researched counting processes. He is also known for his consulting and advocacy on behalf of alleged victims of statistical misrepresentation, including the reversal of the murder conviction of a Dutch nurse who had been jailed for six years.
In probability theory, Chernoff's distribution, named after Herman Chernoff, is the probability distribution of the random variable
Erich Leo Lehmann was a German-born American statistician, who made a major contribution to nonparametric hypothesis testing. He is one of the eponyms of the Lehmann–Scheffé theorem and of the Hodges–Lehmann estimator of the median of a population.
In probability theory a Brownian excursion process is a stochastic process that is closely related to a Wiener process. Realisations of Brownian excursion processes are essentially just realizations of a Wiener process selected to satisfy certain conditions. In particular, a Brownian excursion process is a Wiener process conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. BEPs are important because, among other reasons, they naturally arise as the limit process of a number of conditional functional central limit theorems.
Ulf Grenander was a Swedish statistician and professor of applied mathematics at Brown University.
Gábor J. Székely is a Hungarian-American statistician/mathematician best known for introducing energy statistics (E-statistics). Examples include: the distance correlation, which is a bona fide dependence measure, equals zero exactly when the variables are independent; the distance skewness, which equals zero exactly when the probability distribution is diagonally symmetric; the E-statistic for normality test; and the E-statistic for clustering.
Pranab Kumar Sen was an Indian-American statistician who was a professor of statistics and the Cary C. Boshamer Professor of Biostatistics at the University of North Carolina at Chapel Hill.
In Bayesian inference, the Bernstein–von Mises theorem provides the basis for using Bayesian credible sets for confidence statements in parametric models. It states that under some conditions, a posterior distribution converges in the limit of infinite data to a multivariate normal distribution centered at the maximum likelihood estimator with covariance matrix given by , where is the true population parameter and is the Fisher information matrix at the true population parameter value:
Adrianus Willem "Aad" van der Vaart is a Dutch professor of Stochastics at the Delft Institute of Applied Mathematics at Delft University of Technology.
Michael Barrett Woodroofe was an American probabilist and statistician. He was a professor of statistics and of mathematics at the University of Michigan, where he was the Leonard J. Savage Professor until his retirement. He was noted for his work in sequential analysis and nonlinear renewal theory, in central limit theory, and in nonparametric inference with shape constraints.
Dorota Maria Dabrowska is a Polish statistician known for applying nonparametric statistics and semiparametric models to counting processes and survival analysis. Dabrowska's estimator, from her paper "Kaplan–Meier estimate on the plane" is a widely used tool for bivariate survival under random censoring.
Charles "Chuck" Joel Stone was an American statistician and mathematician.
Marloes Henriette Maathuis is a Dutch statistician known for her work on causal inference using graphical models, particularly in high-dimensional data from applications in biology and epidemiology. She is a professor of statistics at ETH Zurich in Switzerland.
Jon August Wellner is an American statistician known for his contributions to the fields of statistical inference, empirical process theory, and survival analysis.
