Related papers: Sequential block bootstrap in a Hilbert space with…
In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2-Wasserstein space…
Choi and Shin (2020) have constructed a bootstrap-based test for change-points in panels with temporal and and/or cross-sectional dependence. They have compared their test to several other proposed tests. We demonstrate that by an…
We consider inference problems for high-dimensional (HD) functional data with a dense number (T) of repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal…
Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a…
Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…
We numerically study bootstrap percolation on Kleinberg's spatial networks, in which the probability density function of a node to have a long-range link at distance $r$ scales as $P(r)\sim r^{\alpha}$. Setting the ratio of the size of the…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap…
We establish central limit theorems for principal eigenvalues and eigenvectors under a large factor model setting, and develop two-sample tests of both principal eigenvalues and principal eigenvectors. One important application is to detect…
We carefully bootstrap the crossing kernels of Virasoro conformal blocks from first principles. Our approach emphasizes the Hilbert space structure of the space of Virasoro conformal blocks which makes the consistency of crossing…
Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
A common feature in many neuroscience datasets is the presence of hierarchical data structures, most commonly recording the activity of multiple neurons in multiple animals across multiple trials. Accordingly, the measurements constituting…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
We consider the problem of testing the stationarity and isotropy of a spatial point pattern based on the concept of local spectra. Using a logarithmic transformation, the mechanism of the proposed test is approximately identical to a simple…
In this paper, we propose an easy-to-implement residual-based specification testing procedure for detecting structural changes in factor models, which is powerful against both smooth and abrupt structural changes with unknown break dates.…
It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation functions of four scalars. All…
In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators.…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: conventional critical values based on asymptotics often lead to…