Approximation of probability distributions by convex mixtures of Gaussian measures

By Athanassia G. Bacharoglou. 2010

55 citations recorded by the source corpus.

. Let A + = { a = ( a n ) ∈ (cid:2) p> 1 (cid:2) p : a n > 0 , ∀ n ∈ N } and let { φ j } ∞ j =1 be an enumeration of all normal distributions with mean a rational number and variance 1 n 2 , n = 1 , 2 ... . We prove that there exists an a ∈ A + such that every probability density function, continuous, with compact support in R , can be approximated in L 1 and L ∞ norm simultaneously by the averages 1 (cid:3) nj =1 a j (cid:3) nj =1 a j φ j . The set of such sequences is a dense G δ set in A + and contains a dense positive cone.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e2b3ce2e0d66238fba443abece60641f98036114