Spectral distribution of large generalized random kernel matrices

Publication date: Available online 9 May 2019Source: Statistics & Probability LettersAuthor(s): Xingyuan ZengAbstractWe consider n×n random kernel matrix An whose entries are of form F(Xi,Xj)−unδij∑kF(Xi,Xk) with F(X,Y)=f(X′Y∕p) or f(|X−Y|2∕p) for i.i.d. random vectors Xi=Σp1∕2Yi∈Rp. Here f is a real-valued function, un is any real number which is allowed to change with n, Σp is a p×p positive semi-definite matrix and the entries of Yi’s are i.i.d. mean 0, variance 1 and have bounded m
(m>4) absolute moments. Explicit limits of spectral distributions of generalized random kernel matrices are obtained in the case of p∕n→γ∈(0,∞) as p,n→∞.

Source: Statistics and Probability Letters - May 10, 2019 Category: Statistics Source Type: research