arXiv subjects

Roland Fried

Publications and source records attributed to Roland Fried.

At least 19 recordsLinked to original sources

arXiv2026

glmSTARMA -- An R-Package for fitting autoregressive spatio-temporal models following generalized linear models

The R package glmSTARMA implements autoregressive models for spatio-temporal data at fixed locations, with time-invariant spatial dependency structure. We rely on generalized linear models methodology and unify several approaches for the analysis of spatial count time series. Such models allow the (conditional) mean of the response to depend on past observations, lagged (conditional) expectations, and covariates. The response can be a continuous or a discrete random variable. Additionally, the package develops inference for double generalized linear models, allowing the dispersion parameter(s) of the marginal distributions to be modeled similarly to the mean process. This is a new capability which introduces, for example, spatio-temporal volatility models, such as space-time GARCH processes, and count time series models with spatio-temporal overdispersion and underdispersion. We provide functions for model estimation, simulation, inference, and prediction. Its use is illustrated by data examples.

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arXiv2026

A robust nonparametric test for spatial isotropy in lattice data

This paper proposes a robust test for assessing isotropy based on the variogram of spatial data on a two-dimensional regular grid. The test is based on the non-robust subsampling test for isotropy of Guan et al. (2004), which uses the idea of comparing variogram estimates in diff erent directions at the same distance. The robust test employs robust variogram esti- mators which are based on estimators of univariate or multivariate scatter and perform well in the presence of isolated or block outliers. Additionally, a diff erent resampling method, called block permutation, is proposed. Compared with the subsampling test, the block per- mutation test maintains the signifi cance level even for strong dependencies in the data and is robust to outliers. The methods are illustrated by an application to Landsat 8 satellite data, where outlier blocks may occur due to, for example, clouds.

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arXiv2025

Detecting changes in the mean of spatial random fields on a regular grid

We propose statistical procedures for detecting changes in the mean of spatial random fields observed on regular grids. The proposed framework provides a general approach to change detection in spatial processes. Extending a block-based method originally developed for time series, we introduce two test statistics, one based on Gini's mean difference and a novel variance-based variant. Under mild moment conditions, we derive asymptotic normality of the variance-based statistic and prove its consistency against almost all non-constant mean functions (in a sense of positive Lebesgue measure). To accommodate spatial dependence, we modify our procedures for M-dependent data and we further develop a de-correlation algorithm based on estimated autocovariances. Monte Carlo simulations demonstrate that the tests maintain appropriate size and power for both independent and dependent data. In an application to satellite images, especially our variance-based test reliably detects regions undergoing deforestation.

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arXiv2025

Parameter Estimation and Seasonal Modification of the Fractional Poisson Process with Application to Vorticity Extremes over the North Atlantic

The fractional Poisson process (FPP) generalizes the standard Poisson process by replacing exponentially distributed return times with Mittag-Leffler distributed ones with an extra tail parameter, allowing for greater flexibility. The FPP has been applied in various fields, such as modeling occurrences of extratropical cyclones in meteorology and solar flares in physics. We propose a new estimation method for the parameters of the FPP, based on minimizing the distance between the empirical and the theoretical distribution at selected quantiles. We conduct an extensive simulation study to evaluate the advantages and limitations of the new estimation method and to compare it with several competing estimators, some of which have not yet been examined in the Mittag-Leffler setting. To enhance the applicability of the FPP in real-world scenarios, particularly in meteorology, we propose a method for incorporating seasonality into the FPP through distance-based weighting. We then analyze the return times of relative vorticity extremes in the North Atlantic-European region using our seasonal modeling approach.

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arXiv2025

Probabilistic Time Series Forecasting of Residential Loads -- A Copula Approach

Predicting the time series of future evolutions of renewable injections and demands is of utmost importance for the operation of power systems. However, the current state of the art is mostly focused on mean-value time series predictions and only very few methods provide probabilistic forecasts. In this paper, we rely on kernel density estimation and vine copulas to construct probabilistic models for individual load profiles of private households. Our approach allows the quantification of variability of individual energy consumption in general and of daily peak loads in particular. We draw upon an Australian distribution grid dataset to illustrate our findings. We generate synthetic loads that follow the distribution of the real data.

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arXiv2024

Nonparametric directional variogram estimation in the presence of outlier blocks

This paper proposes robust estimators of the variogram, a statistical tool that is commonly used in geostatistics to capture the spatial dependence structure of data. The new estimators are based on the highly robust minimum covariance determinant estimator and estimate the directional variogram for several lags jointly. Simulations and breakdown considerations confirm the good robustness properties of the new estimators. While Genton's estimator based on the robust estimation of the variance of pairwise sums and differences performs well in case of isolated outliers, the new estimators based on robust estimation of multivariate variance and covariance matrices perform superior to the established alternatives in the presence of outlier blocks in the data. The methods are illustrated by an application to satellite data, where outlier blocks may occur because of e.g. clouds.

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arXiv2024

Spatio-temporal count autoregression

We study the problem of modeling and inference for spatio-temporal count processes. Our approach uses parsimonious parameterisations of multivariate autoregressive count time series models, including possible regression on covariates. We control the number of parameters by specifying spatial neighbourhood structures for possibly huge matrices that take into account spatio-temporal dependencies. This work is motivated by real data applications which call for suitable models. Extensive simulation studies show that our approach yields reliable estimators.

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arXiv2023

Models for temporal clustering of extreme events with applications to mid-latitude winter cyclones

The occurrence of extreme events like heavy precipitation or storms at a certain location often shows a clustering behaviour and is thus not described well by a Poisson process. We construct a general model for the inter-exceedance times in between extreme events which combines different candidate models for such behaviour. One of them is formulated in terms of clusters of dependent events with exponential inter-exceedance times in between clusters, while the other assumes independent events separated by heavy-tailed inter-exceedance times. We propose a modification of the Cram\'er-von Mises distance for fitting the combined model. The resulting estimator turns out to be competitive with specialised estimators if the data stem from one of the two submodels. Our modelling approach thus allows us to distinguish these different data generating mechanisms without the need of a-priori model selection. An application to mid-latitude winter cyclones illustrates the usefulness of our work as the combination of the two mechanisms improves the descriptions of such occurrences at many places.

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arXiv2023

Intervention analysis for integer-valued autoregressive models

We study the problem of intervention effects generating various types of outliers in an integer-valued autoregressive model with Poisson innovations. We concentrate on outliers which enter the dynamics and can be seen as effects of extraordinary events. We consider three different scenarios, namely the detection of an intervention effect of a known type at a known time, the detection of an intervention effect of unknown type at a known time and the detection of an intervention effect when both the type and the time are unknown. We develop F-tests and score tests for the first scenario. For the second and third scenarios we rely on the maximum of the different F-type or score statistics. The usefulness of the proposed approach is illustrated using monthly data on human brucellosis infections in Greece.

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arXiv2021

An Asymptotic Test for Constancy of the Variance under Short-Range Dependence

We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic, we establish new limit theorems for U-statistics of dependent triangular arrays. We derive the asymptotic distribution of the test statistic under the null hypothesis of a constant variance and show that the test is consistent against a large class of alternatives, including multiple structural breaks in the variance. Our test is applicable even in the case of non-stationary processes, assuming a locally stationary mean function. The performance of the test and its comparatively low computation time are illustrated in an extensive simulation study. As an application, we analyse Google Trends data, monitoring the relative search interest for the topic "global warming."

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arXiv2020

QANOVA: Quantile-based Permutation Methods For General Factorial Designs

Population means and standard deviations are the most common estimands to quantify effects in factorial layouts. In fact, most statistical procedures in such designs are built towards inferring means or contrasts thereof. For more robust analyses, we consider the population median, the interquartile range (IQR) and more general quantile combinations as estimands in which we formulate null hypotheses and calculate compatible confidence regions. Based upon simultaneous multivariate central limit theorems and corresponding resampling results, we derive asymptotically correct procedures in general, potentially heteroscedastic, factorial designs with univariate endpoints. Special cases cover robust tests for the population median or the IQR in arbitrary crossed one-, two- and higher-way layouts with potentially heteroscedastic error distributions. In extensive simulations we analyze their small sample properties and also conduct an illustrating data analysis comparing children's height and weight from different countries.

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arXiv2019

A Robust Method for Shift Detection in Time Series

We present a robust test for change-points in time series which is based on the two-sample Hodges-Lehmann estimator. We develop new limit theory for a class of statistics based on the two-sample U-quantile processes, in the case of short range dependent observations. Using this theory we can derive the asymptotic distribution of our test statistic under the null hypothesis. We study the finite sample properties of our test via a simulation study and compare the test with the classical CUSUM test and a test based on the Wilcoxon-Mann-Whitney statistic.

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arXiv2019

Robust change point tests by bounded transformations

Classical moment based change point tests like the cusum test are very powerful in case of Gaussian time series with one change point but behave poorly under heavy tailed distributions and corrupted data. A new class of robust change point tests based on cusum statistics of robustly transformed observations is proposed. This framework is quite flexible, depending on the used transformation one can detect for instance changes in the mean, scale or dependence of a possibly multivariate time series. Simulations indicate that this approach is very powerful in detecting changes in the marginal variance of ARCH processes and outperforms existing proposals for detecting structural breaks in the dependence structure of heavy tailed multivariate time series.

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arXiv2017

Robust change-point detection in panel data

In panel data we observe a usually high number N of individuals over a time period T. Even if T is large one often assumes stability of the model over time. We propose a nonparametric and robust test for a change in location and derive its asymptotic distribution under short range dependence and for N, T tending to infinity. Some simulations show its usefulness under heavy tailed distributions.

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arXiv2017

Dealing with seasonal variability and inter-site dependence in regional flood frequency analysis

This paper considers the regional estimation of high quantiles of annual maximal river flow distributions $F$, an important problem from flood frequency analysis. Even though this particular problem has been addressed by many papers, less attention has been payed to incorporating seasonal variability and spatial dependence into the methods. We are going to discuss two regional estimators of high quantiles of local distributions $F$ that are able to deal with these important features, namely, a parametric approach based on so-called two-component extreme value distributions and a semi-parametric approach based on regional estimation of a tail index. The asymptotic normality of the estimators is derived for both procedures, which for instance enables us to account for estimation uncertainty without the need of parametric dependence models or bootstrap procedures. A comprehensive simulation study is conducted and our main findings are illustrated on river flow series from the Mulde basin in Germany, where people have suffered several times from severe floods over the last 100 years.

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arXiv2016

The spatial sign covariance matrix and its application for robust correlation estimation

We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case was used to construct the spatial sign correlation coefficient, which is a non-parametric and robust estimator for the correlation coefficient within the elliptical model. We consider a multivariate generalization, which we call the multivariate spatial sign correlation matrix.

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arXiv2016

Beyond unimodal regression: modelling multimodality with piecewise unimodal regression or deconvolution models

Shape constraints enable us to reflect prior knowledge in regression settings. A unimodality constraint, for example, can describe the frequent case of a first increasing and then decreasing intensity. Yet, data shapes often exhibit multiple modes. Therefore, we go beyond unimodal regression and propose modelling multimodality with piecewise unimodal regression or with deconvolution models based on unimodal peak shapes. Usefulness of unimodal regression and its multimodal extensions is demonstrated within three applications areas: marine biology, astroparticle physics and breath gas analysis. Despite this diversity, valuable results are obtained in each application. This encourages the use of these methods in other areas as well.

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arXiv2015

Elliptical graphical modelling

We propose elliptical graphical models based on conditional uncorrelatedness as a general- ization of Gaussian graphical models by letting the population distribution be elliptical instead of normal, allowing the fitting of data with arbitrarily heavy tails. We study the class of propor- tionally affine equivariant scatter estimators and show how they can be used to perform elliptical graphical modelling, leading to a new class of partial correlation estimators and analogues of the classical deviance test. General expressions for the asymptotic variance of partial correla- tion estimators, unconstrained and under decomposable models, are given, and the asymptotic chi square approximation of the pseudo-deviance test statistic is proved. The feasibility of our approach is demonstrated by a simulation study, using, among others, Tyler's scatter estimator, which is distribution-free within the elliptical model. Our approach provides a robustification of Gaussian graphical modelling. The latter is likelihood-based and known to be very sensitive to model misspecification and outlying observations.

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