Nonparametric Risk Assessment and Density Estimation for Persistence Landscapes

TL;DR

This paper introduces a bootstrap-based method for constructing confidence intervals for persistence landscapes, utilizing kernel density estimation and IMSE evaluation, demonstrating improved accuracy through simulations and real data analysis.

Contribution

It develops a novel bootstrap approach for confidence intervals in persistence landscapes, incorporating kernel density estimation and IMSE, with algorithms and empirical validation.

Findings

Significant improvement over standard confidence interval methods

Effective kernel density estimation for persistence landscapes

Validated accuracy through simulations and real data

Abstract

This paper presents approximate confidence intervals for each function of parameters in a Banach space based on a bootstrap algorithm. We apply kernel density approach to estimate the persistence landscape. In addition, we evaluate the quality distribution function estimator of random variables using integrated mean square error (IMSE). The results of simulation studies show a significant improvement achieved by our approach compared to the standard version of confidence intervals algorithm. In the next step, we provide several algorithms to solve our model. Finally, real data analysis shows that the accuracy of our method compared to that of previous works for computing the confidence interval.