DENSITY ESTIMATION IN RKHS WITH APPLICATION TO KOROBOV SPACES IN HIGH DIMENSIONS

A kernel method for estimating a probability density function from an independent and identically distributed sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear equation. An error analysis for the mean integrated squared error is established in a general reproducing kernel Hilbert space setting. The theory developed is then applied to estimate probability density func-tions belonging to weighted Korobov spaces, for which a dimension-independent convergence rate is established. Under a suitable smoothness assumption, our method attains a rate arbitrarily close to the optimal rate. Numerical results support our theory.

Automated summary

The paper presents a kernel method for estimating a probability density function from an independent and identically distributed sample. The estimator is a linear combination of kernel functions with coefficients determined by a linear equation. An error analysis is conducted for the mean integrated squared error in a general reproducing kernel Hilbert space setting. The developed theory is then applied to estimate probability density functions in weighted Korobov spaces, achieving a dimension-independent convergence rate close to the optimal rate. Numerical results validate the theory.