Nonparametric Risk Assessment and Density Estimation for Persistence Landscapes
This work provides improved statistical tools for topological data analysis, specifically for persistence landscapes, which is an incremental advancement in this domain.
The paper tackles the problem of risk assessment and density estimation for persistence landscapes by developing approximate confidence intervals using a bootstrap algorithm and kernel density estimation. The results show significant improvement over standard confidence interval algorithms in simulation studies and higher accuracy compared to previous methods in real data analysis.
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.