Bona fide Riesz projections for density estimation
This addresses a technical limitation in density estimation for statistical applications, though it appears to be an incremental improvement over existing projection methods.
The paper tackles the problem of probability density estimation using projection methods by proposing a Riesz projection operator that guarantees bona fide properties (non-negativity and total probability mass 1), with results showing improved performance in scenarios prone to rippling effects.
The projection of sample measurements onto a reconstruction space represented by a basis on a regular grid is a powerful and simple approach to estimate a probability density function. In this paper, we focus on Riesz bases and propose a projection operator that, in contrast to previous works, guarantees the bona fide properties for the estimate, namely, non-negativity and total probability mass $1$. Our bona fide projection is defined as a convex problem. We propose solution techniques and evaluate them. Results suggest an improved performance, specifically in circumstances prone to rippling effects.