Zobrazeno 1 - 10
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pro vyhledávání: '"Krebs, A. T."'
Functional times series have become an integral part of both functional data and time series analysis. This paper deals with the functional autoregressive model of order 1 and the autoregression bootstrap for smooth functions. The regression operator
Externí odkaz:
http://arxiv.org/abs/1811.06172
Autor:
Krebs, Johannes T. N.
We consider the double functional nonparametric regression model $Y=r(X)+\epsilon$, where the response variable $Y$ is Hilbert space-valued and the covariate $X$ takes values in a pseudometric space. The data satisfy an ergodicity criterion which dat
Externí odkaz:
http://arxiv.org/abs/1806.10196
Autor:
Krebs, Johannes T. N.
In this manuscript we present exponential inequalities for spatial lattice processes which take values in a separable Hilbert space and satisfy certain dependence conditions. We consider two types of dependence: spatial data under $\alpha$-mixing con
Externí odkaz:
http://arxiv.org/abs/1708.08505
In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It can be useful to obtain consistency properties for no
Externí odkaz:
http://arxiv.org/abs/1702.02023
Autor:
Krebs, Johannes T. N.
We give a new large deviation inequality for sums of random variables of the form $Z_k = f(X_k,X_t)$ for $k,t\in \mathbb{N}$, $t$ fixed, where the underlying process $X$ is $\beta$-mixing. The inequality can be used to derive concentration inequaliti
Externí odkaz:
http://arxiv.org/abs/1701.05380
Autor:
Krebs, Johannes T. N.
In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in highly-connected netwo
Externí odkaz:
http://arxiv.org/abs/1701.04188
Consistency and Asymptotic Normality of Stochastic Euler Schemes for Ordinary Differential Equations
Autor:
Krebs, Johannes T. N.
Publikováno v:
Statistics & Probability Letters, 125, 1-8 (2017)
General stochastic Euler schemes for ordinary differential equations are studied. We give proofs on the consistency, the rate of convergence and the asymptotic normality of these procedures.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/1609.06880
Autor:
Krebs, Johannes T. N.
Nonparametric density estimators are studied for $d$-dimensional, strongly spatial mixing data which is defined on a general $N$-dimensional lattice structure. We consider linear and nonlinear hard thresholded wavelet estimators which are derived fro
Externí odkaz:
http://arxiv.org/abs/1609.06830
Autor:
Krebs, Johannes T. N.
We study a nonparametric regression model for sample data which is defined on an $N$-dimensional lattice structure and which is assumed to be strong spatial mixing: we use design adapted multidimensional Haar wavelets which form an orthonormal system
Externí odkaz:
http://arxiv.org/abs/1609.06865
Autor:
Krebs, Johannes T. N.
We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The rates are op
Externí odkaz:
http://arxiv.org/abs/1609.06744