# Category: Empirical process

Empirical process
In probability theory, an empirical process is a stochastic process that describes the proportion of objects in a system in a given state.For a process in a discrete state space a population continuou
In statistics, the Khmaladze transformation is a mathematical tool used in constructing convenient goodness of fit tests for hypothetical distribution functions. More precisely, suppose are i.i.d., po
Empirical distribution function
In statistics, an empirical distribution function (commonly also called an empirical Cumulative Distribution Function, eCDF) is the distribution function associated with the empirical measure of a sam
Donsker's theorem
In probability theory, Donsker's theorem (also known as Donsker's invariance principle, or the functional central limit theorem), named after Monroe D. Donsker, is a functional extension of the centra
Komlós–Major–Tusnády approximation
In probability theory, the Komlós–Major–Tusnády approximation (also known as the KMT approximation, the KMT embedding, or the Hungarian embedding) refers to one of the two strong embedding theorems: 1
Shattered set
The concept of shattered sets plays an important role in Vapnik–Chervonenkis theory, also known as VC-theory. Shattering and VC-theory are used in the study of empirical processes as well as in statis
Vapnik–Chervonenkis theory
Vapnik–Chervonenkis theory (also known as VC theory) was developed during 1960–1990 by Vladimir Vapnik and Alexey Chervonenkis. The theory is a form of computational learning theory, which attempts to
Pregaussian class
In probability theory, a pregaussian class or pregaussian set of functions is a set of functions, square integrable with respect to some probability measure, such that there exists a certain Gaussian
Intensity-duration-frequency curve
An intensity-duration-frequency curve (IDF curve) is a mathematical function that relates the rainfall intensity with its duration and frequency of occurrence. These curves are commonly used in hydrol
Dvoretzky–Kiefer–Wolfowitz inequality
In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz–Massart inequality (DKW inequality) bounds how close an empirically determined distribution function will be to the distribu
Empirical measure
In probability theory, an empirical measure is a random measure arising from a particular realization of a (usually finite) sequence of random variables. The precise definition is found below. Empiric
Brownian bridge
A Brownian bridge is a continuous-time stochastic process B(t) whose probability distribution is the conditional probability distribution of a standard Wiener process W(t) (a mathematical model of Bro
CDF-based nonparametric confidence interval
In statistics, cumulative distribution function (CDF)-based nonparametric confidence intervals are a general class of confidence intervals around statistical functionals of a distribution. To calculat
Glivenko–Cantelli theorem
In the theory of probability, the Glivenko–Cantelli theorem (sometimes referred to as the Fundamental Theorem of Statistics), named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli, determ