Related papers: Block bootstrap for the empirical process of long-…
The use of quadratic forms of the empirical process for the two-sample problem in the context of functional data is considered. The convergence of the family of statistics proposed to a Gaussian limit is established under metric entropy…
Let $(X_j)_{j\geq1}$ be a multivariate long-range dependent Gaussian process. We study the asymptotic behavior of the corresponding sequential empirical process indexed by a class of functions. If some entropy condition is satisfied we have…
We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an…
Focusing on a high dimensional linear model $y = X\beta + \epsilon$ with dependent, non-stationary, and heteroskedastic errors, this paper applies the debiased and threshold ridge regression method that gives a consistent estimator for…
We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are…
We investigate asymptotic inference in a linear regression model where both response and regressors are functions, using an estimator based on functional principal components analysis. Although this approach is widely used in functional…
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…
To address the difficult problem of multi-step ahead prediction of non-parametric autoregressions, we consider a forward bootstrap approach. Employing a local constant estimator, we can analyze a general type of non-parametric time series…
We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…
We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…
In unit root testing, a piecewise locally stationary process is adopted to accommodate nonstationary errors that can have both smooth and abrupt changes in second- or higher-order properties. Under this framework, the limiting null…
A general notion of bootstrapped $\phi$-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrapped $\phi$-divergence estimates are obtained, by mean of the…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
A workload model using the infinite source Poisson model for bursts is combined with the on--off model for within burst activity. Burst durations and on--off durations are assumed to have heavy-tailed distributions with infinite variance…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
Natural and social multivariate systems are commonly studied through sets of simultaneous and time-spaced measurements of the observables that drive their dynamics, i.e., through sets of time series. Typically, this is done via hypothesis…
The empirical beta copula is a simple but effective smoother of the empirical copula. Because it is a genuine copula, from which, moreover, it is particularly easy to sample, it is reasonable to expect that resampling procedures based on…
AI/ML methods are increasingly used in economics to generate binary variables (or labels) via classification algorithms. When these generated variables are included as covariates in regressions, even small misclassification errors can…
Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response…