In theory of probability, the Komlós–Major–Tusnády approximation (also known as the KMT approximation, the KMT embedding, or the Hungarian embedding) is an approximation of the empirical process by a Gaussian process constructed on the same probability space. It is named after Hungarian mathematicians János Komlós, Gábor Tusnády, and Péter Major.
Let be independent uniform (0,1) random variables. Define a uniform empirical distribution function as
Define a uniform empirical process as
The Donsker theorem (1952) shows that converges in law to a Brownian bridge Komlós, Major and Tusnády established a sharp bound for the speed of this weak convergence.
A corollary of that theorem is that for any real iid r.v. with cdf it is possible to construct a probability space where independent sequences of empirical processes and Gaussian processes exist such that