arXiv subjects

Roland Fried

Publications and source records attributed to Roland Fried.

22 records · Page 2Linked to original sources

arXiv2015

Estimation of the variance of partial sums of dependent processes

We study subsampling estimators for the limit variance \[ σ^2=Var(X_1)+2 \sum_{k=2}^\infty Cov(X_1,X_k) \] of partial sums of a stationary stochastic process $(X_k)_{k\geq 1}$. We establish $L_2$-consistency of a non-overlapping block resampling method. Our results apply to processes that can be represented as functionals of strongly mixing processes. Motivated by recent applications to rank tests, we also study estimators for the series $Var(F(X_1))+2 \sum_{k=2}^\infty Cov(F(X_1),F(X_k))$, where $F$ is the distribution function of $X_1$. Simulations illustrate the usefulness of the proposed estimators and of a mean squared error optimal rule for the choice of the block length.

math.ST↗

arXiv2014

Multivariate Generalized Linear-statistics of short range dependent data

Generalized linear (GL-) statistics are defined as functionals of an U-quantile process and unify different classes of statistics such as U-statistics and L-statistics. We derive a central limit theorem for GL-statistics of strongly mixing sequences and arbitrary dimension of the underlying kernel. For this purpose we establish a limit theorem for U-statistics and an invariance principle for U-processes together with a convergence rate for the remaining term of the Bahadur representation. An application is given by the generalized median estimator for the tail-parameter of the Pareto distribution, which is commonly used to model exceedances of high thresholds. We use subsampling to calculate confidence intervals and investigate its behaviour under independence and strong mixing in simulations.

math.ST↗

arXiv2014

Spatial Sign Correlation

A new robust correlation estimator based on the spatial sign covariance matrix (SSCM) is proposed. We derive its asymptotic distribution and influence function at elliptical distributions. Finite sample and robustness properties are studied and compared to other robust correlation estimators by means of numerical simulations.

stat.ME↗

arXiv2013

Change-Point Detection under Dependence Based on Two-Sample U-Statistics

We study the detection of change-points in time series. The classical CUSUM statistic for detection of jumps in the mean is known to be sensitive to outliers. We thus propose a robust test based on the Wilcoxon two-sample test statistic. The asymptotic distribution of this test can be derived from a functional central limit theorem for two-sample U-statistics. We extend a theorem of Csorgo and Horvath to the case of dependent data.

math.ST↗