Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive confidence sets for persistence dia...

We demonstrate that feedback in discrete memoryless channels has the capability of greatly lowering the block error rate of codes designed for open-loop operation. First we show how to use full feedback of the channel output to turn any capacity achieving code into a reliability-function achieving code. Second, we propose a practical embodiment based on sparse-graph codes, belief propagation, a...

Confidence intervals in econometric time series regressions suffer from notorious coverage problems. This is especially true when the dependence in the data is noticeable and sample sizes are small to moderate, as is often the case in empirical studies. This paper suggests using the studentized block bootstrap and discusses practical issues, such as the choice of the block size. A particular da...

Theory in time series analysis is often developed in the context of nite-dimensional models for the data generating process. Whereas corresponding estimators such as those of a conditional mean function are reasonable even if the true dependence mechanism is of a more complex structure, it is usually necessary to capture the whole dependence structure asymptotically for the bootstrap to be vali...

Abstract The portmanteau test provides the vanilla method for detecting serial correlations in classical univariate time series analysis. is extended to case of observations from a locally stationary functional series. Asymptotic critical values are obtained by suitable block multiplier bootstrap procedure. shown asymptotically hold its level and be consistent against general alternatives.

The concept of the autoregressive (AR) sieve bootstrap is investigated for the case of spatial processes in Z. This procedure fits AR models of increasing order to the given data and, via resampling of the residuals, generates bootstrap replicates of the sample. The paper explores the range of validity of this resampling procedure and provides a general check criterion which allows to decide wh...

In this work, we develop conformal bootstrap for Galilean field theory (GCFT). a GCFT, the Hilbert space could be decomposed into quasiprimary states and its global descendants. Different from usual theory, quasi-primary in GCFT constitute multiplets, which are block-diagonized under boost operator. More importantly multiplets include of negative norms, indicating is not unitary. We compute blo...