Related papers: The Sequential Empirical Process of Nonlinear Long…
We consider statistical inference in high-dimensional regression problems under affine constraints on the parameter space. The theoretical study of this is motivated by the study of genetic determinants of diseases, such as diabetes, using…
For $n$ equidistant observations of a L\'evy process at time distance $\Delta_n$ we consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal-Getoor index in a non- or semiparametric manner.…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is…
In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the…
Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…
Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$,…
Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…
Consider a non--linear function $G(X_t)$ where $X_t$ is a stationary Gaussian sequence with long--range dependence. The usual reduction principle states that the partial sums of $G(X_t)$ behave asymptotically like the partial sums of the…
For $\{X(t), t \in G_\delta\}$ a centered Gaussian process with stationary increments and a.s. sample paths on a discrete grid $G_\delta=\{0,\delta,2\delta, ...\}$, where $\delta>0$, we investigate the stationary reflected process…
Binomial time series in which the logit of the probability of success is modelled as a linear function of observed regressors and a stationary latent Gaussian process are considered. Score tests are developed to first test for the existence…
We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all…
We study approximations of non-Gaussian stationary processes having long range correlations with microcanonical models. These models are conditioned by the empirical value of an energy vector, evaluated on a single realization. Asymptotic…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range…
We study the short-time asymptotical behavior of stochastic flows on \mathbb{R} in the \sup-norm. The results are stated in terms of a Gaussian process associated with the covariation of the flow. In case the Gaussian process has a…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
In this paper, we study the asymptotic relation between the maximum of acontinuous order statistics process formed by stationary Gaussian processesand the maximum of this process sampled at discrete time points. It is shown that, these two…
We define Gaussian assignment process, determine the asymptotic behavior of its maximum's expectation and suggest an explicit strategy that attains the corresponding asymptotics.