Sharpen Laplace-NPMLE support-size bounds

Sharpen the support-size characterization of the nonparametric maximum likelihood estimator under the Laplace convolution model by establishing bounds comparable to the logarithmic support-size bounds known for Gaussian mixtures.

Background

The paper proves that every NPMLE under the bounded one-dimensional Laplace convolution model can be represented with support contained in the projected observation set, which gives an upper bound of at most n candidate support locations. However, this structural result does not determine the number of support points that receive positive estimated weight.

For Gaussian mixtures, prior work establishes support-size bounds of logarithmic order in the sample size with high probability. The paper reports empirical evidence that the active support size for Laplace mixtures may grow faster than logarithmically, but does not provide a corresponding asymptotic theorem. The open problem is therefore to obtain sharp support-size bounds for the Laplace NPMLE and clarify whether its behavior fundamentally differs from the Gaussian case.