Related papers: Volterra bootstrap: Resampling higher-order statis…

We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-invariant systems, this class covers nonlinear systems modeled…

Pooled logistic regression models are commonly applied in survival analysis. However, the standard implementation can be computationally demanding, which is further exacerbated when using the nonparametric bootstrap for inference. To ease…

This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The…

We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…

We consider semiparametric transformation models, where after pre-estimation of a parametric transformation of the response the data are modeled by means of nonparametric regression. We suggest subsequent procedures for testing lack-of-fit…

Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…

Existing frequency domain methods for bootstrapping time series have a limited range. Consider for instance the class of spectral mean statistics (also called integrated periodograms) which includes many important statistics in time series…

This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…

The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…

Modern problems in statistics tend to include estimators of high computational complexity and with complicated distributions. Statistical inference on such estimators usually relies on asymptotic normality assumptions, however, such…

This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…

We introduce a novel and efficient simulation scheme for Hawkes processes on a fixed time grid, leveraging their affine Volterra structure. The key idea is to first simulate the integrated intensity and the counting process using Inverse…

Volterra analysis and its variants have long been prominent among methods for modeling multi-input non-linear systems. The product of Volterra analysis, the Volterra kernels, are particularly suited to quantifying intra- and inter-input…

In this paper, we propose a novel bootstrap algorithm that is more efficient than existing methods for approximating the distribution of the factor-augmented regression estimator for a rotated parameter vector. The regression is augmented…

We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go…

The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly…

Simultaneous inference for high-dimensional non-Gaussian time series is always considered to be a challenging problem. Such tasks require not only robust estimation of the coefficients in the random process, but also deriving limiting…