  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.
