Maciej Gocwin | Searcharxiv

arXiv2006

Simultaneous confidence bands for the integrated hazard function

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson--Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Two methods of construction of such confidence bands are proposed. The weird bootstrap method is used for resampling. Simulations are made to compare the actual coverage probability of the bootstrap and the asymptotic simultaneous confidence bands. It is shown that the equal--tailed bootstrap confidence band has the coverage probability closest to the nominal one. We also present application of our confidence bands to the data regarding survival after heart transplant.

math.ST↗

arXiv2005

On the Complexity of Searching Maximum of a Function on a Quantum Computer

We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the algorithm for finding maximum of a discrete sequence. To prove lower bounds we use results for finding logical OR of sequence of bits. We show that quantum computation yields a quadratic speed-up over deterministic and randomized algorithms.

quant-ph↗