arXiv subjects

Carsten Jentsch

Publications and source records attributed to Carsten Jentsch.

At least 19 recordsLinked to original sources

arXiv2026

Resampling simplicial depth

The simplicial depth (SD) is a commonly used indicator of the centrality of points $x\in\mathbb{R}^d$ with respect to distributions $P$ on $\mathbb{R}^d$. Asymptotic theory for the sample SD is based on its representation as a $U$-statistic, which can be either non-degenerate or degenerate. For $d=2$, we prove under mild conditions that this $U$-statistic is degenerate with rate $n$ if and only if $x$ is a center of symmetry of $P$. Otherwise, the asymptotic distribution of SD is non-degenerate with rate $\sqrt{n}$. Because the location of the center of symmetry of $P$ is usually unknown, these two modes of behavior complicate the estimation of the sample distribution of SD at $x$. We propose a two-step adaptive subsampling procedure for estimating that distribution. First, an estimator $\widehat \gamma$ of a parameter $\gamma\in\{1/2, 1\}$ characterizing the correct rate of convergence $n^\gamma$ of SD is constructed based on subsampling. Our estimator uses a bias correction suitable for $U$-statistics. Second, $\widehat \gamma$ is employed for approximating the distribution of the sample SD. We prove the consistency of this subsampling approach and illustrate its usefulness (i) in the construction of confidence intervals for SD, and (ii) in an SD-based supervised classification task

stat.ME↗

arXiv2026

Word-Centered Semantic Graphs for Interpretable Diachronic Sense Tracking

We propose an interpretable, graph-based framework for analyzing semantic shift in diachronic corpora. For each target word and time slice, we induce a word-centered semantic network that integrates distributional similarity from diachronic Skip-gram embeddings with lexical substitutability from time-specific masked language models. We identify sense-related structure by clustering the peripheral graph, align clusters across time via node overlap, and track change through cluster composition and normalized cluster mass. In an application study on a corpus of New York Times Magazine articles (1980 - 2017), we show that graph connectivity reflects polysemy dynamics and that the induced communities capture contrasting trajectories: event-driven sense replacement (trump), semantic stability with cluster over-segmentation effects (god), and gradual association shifts tied to digital communication (post). Overall, word-centered semantic graphs offer a compact and transparent representation for exploring sense evolution without relying on predefined sense inventories.

cs.CL↗

arXiv2025

Structural Periodic Vector Autoregressions

While seasonality inherent to raw macroeconomic data is commonly removed by seasonal adjustment techniques before it is used for structural inference, this may distort valuable information in the data. As an alternative method to commonly used structural vector autoregressions (SVARs) for seasonally adjusted data, we propose to model potential periodicity in seasonally unadjusted (raw) data directly by structural periodic vector autoregressions (SPVARs). This approach does not only allow for periodically time-varying intercepts, but also for periodic autoregressive parameters and innovations variances. As this larger flexibility leads to an increased number of parameters, we propose linearly constrained estimation techniques. Moreover, based on SPVARs, we provide two novel identification schemes and propose a general framework for impulse response analyses that allows for direct consideration of seasonal patterns. We provide asymptotic theory for SPVAR estimators and impulse responses under flexible linear restrictions and introduce a test for seasonality in impulse responses. For the construction of confidence intervals, we discuss several residual-based (seasonal) bootstrap methods and prove their bootstrap consistency under different assumptions. A real data application shows that useful information about the periodic structure in the data may be lost when relying on common seasonal adjustment methods.

econ.EM↗

arXiv2025

Predictive inference for discrete-valued time series

For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we propose to reverse the construction principle by considering preselected sets of interest and estimating the probability that a future observation of the process falls into these sets. The accuracy of the prediction is then evaluated by quantifying the uncertainty associated with estimation of these predictive probabilities. We consider parametric and non-parametric approaches and derive asymptotic theory for the estimators involved. Suitable bootstrap approaches to evaluate the distribution of the estimators considered also are introduced. They have the advantage to imitate the distributions of interest under different possible settings, including the practical important case where uncertainty holds true about the correctness of a parametric model used for prediction. Theoretical justification of the bootstrap is given, which also requires investigation of asymptotic properties of parameter estimators under model misspecification. We elaborate on bootstrap implementations under different scenarios and focus on parametric prediction using INAR and INARCH models and (conditional) maximum likelihood estimators. Simulations investigate the finite sample performance of the predictive method developed and applications to real life data sets are presented.

stat.ME↗

arXiv2025

Joint semi-parametric INAR bootstrap inference for model coefficients and innovation distribution

For modeling the serial dependence in time series of counts, various approaches have been proposed in the literature. In particular, models based on a recursive, autoregressive-type structure such as the well-known integer-valued autoregressive (INAR) models are very popular in practice. The distribution of such INAR models is fully determined by a vector of autoregressive binomial thinning coefficients and the discrete innovation distribution. While fully parametric estimation techniques for these models are mostly covered in the literature, a semi-parametric approach allows for consistent and efficient joint estimation of the model coefficients and the innovation distribution without imposing any parametric assumptions. Although the limiting distribution of this estimator is known, which, in principle, enables asymptotic inference and INAR model diagnostics on the innovations, it is cumbersome to apply in practice. In this paper, we consider a corresponding semi-parametric INAR bootstrap procedure and show its joint consistency for the estimation of the INAR coefficients and for the estimation of the innovation distribution. We discuss different application scenarios that include goodness-of-fit testing, predictive inference and joint dispersion index analysis for count time series. In simulations, we illustrate the finite sample performance of the semi-parametric INAR bootstrap using several innovation distributions and provide real-data applications.

stat.ME↗

arXiv2025

Narrative Shift Detection: A Hybrid Approach of Dynamic Topic Models and Large Language Models

With rapidly evolving media narratives, it has become increasingly critical to not just extract narratives from a given corpus but rather investigate, how they develop over time. While popular narrative extraction methods such as Large Language Models do well in capturing typical narrative elements or even the complex structure of a narrative, applying them to an entire corpus comes with obstacles, such as a high financial or computational cost. We propose a combination of the language understanding capabilities of Large Language Models with the large scale applicability of topic models to dynamically model narrative shifts across time using the Narrative Policy Framework. We apply a topic model and a corresponding change point detection method to find changes that concern a specific topic of interest. Using this model, we filter our corpus for documents that are particularly representative of that change and feed them into a Large Language Model that interprets the change that happened in an automated fashion and distinguishes between content and narrative shifts. We employ our pipeline on a corpus of The Wall Street Journal news paper articles from 2009 to 2023. Our findings indicate that a Large Language Model can efficiently extract a narrative shift if one exists at a given point in time, but does not perform as well when having to decide whether a shift in content or a narrative shift took place.

cs.CL↗

arXiv2025

Identifying economic narratives in large text corpora -- An integrated approach using Large Language Models

As interest in economic narratives has grown in recent years, so has the number of pipelines dedicated to extracting such narratives from texts. Pipelines often employ a mix of state-of-the-art natural language processing techniques, such as BERT, to tackle this task. While effective on foundational linguistic operations essential for narrative extraction, such models lack the deeper semantic understanding required to distinguish extracting economic narratives from merely conducting classic tasks like Semantic Role Labeling. Instead of relying on complex model pipelines, we evaluate the benefits of Large Language Models (LLMs) by analyzing a corpus of Wall Street Journal and New York Times newspaper articles about inflation. We apply a rigorous narrative definition and compare GPT-4o outputs to gold-standard narratives produced by expert annotators. Our results suggests that GPT-4o is capable of extracting valid economic narratives in a structured format, but still falls short of expert-level performance when handling complex documents and narratives. Given the novelty of LLMs in economic research, we also provide guidance for future work in economics and the social sciences that employs LLMs to pursue similar objectives.

econ.GN↗

arXiv2025

ttta: Tools for Temporal Text Analysis

Text data is inherently temporal. The meaning of words and phrases changes over time, and the context in which they are used is constantly evolving. This is not just true for social media data, where the language used is rapidly influenced by current events, memes and trends, but also for journalistic, economic or political text data. Most NLP techniques however consider the corpus at hand to be homogenous in regard to time. This is a simplification that can lead to biased results, as the meaning of words and phrases can change over time. For instance, running a classic Latent Dirichlet Allocation on a corpus that spans several years is not enough to capture changes in the topics over time, but only portraits an "average" topic distribution over the whole time span. Researchers have developed a number of tools for analyzing text data over time. However, these tools are often scattered across different packages and libraries, making it difficult for researchers to use them in a consistent and reproducible way. The ttta package is supposed to serve as a collection of tools for analyzing text data over time.

cs.CL↗

arXiv2024

SpeakGer: A meta-data enriched speech corpus of German state and federal parliaments

The application of natural language processing on political texts as well as speeches has become increasingly relevant in political sciences due to the ability to analyze large text corpora which cannot be read by a single person. But such text corpora often lack critical meta information, detailing for instance the party, age or constituency of the speaker, that can be used to provide an analysis tailored to more fine-grained research questions. To enable researchers to answer such questions with quantitative approaches such as natural language processing, we provide the SpeakGer data set, consisting of German parliament debates from all 16 federal states of Germany as well as the German Bundestag from 1947-2023, split into a total of 10,806,105 speeches. This data set includes rich meta data in form of information on both reactions from the audience towards the speech as well as information about the speaker's party, their age, their constituency and their party's political alignment, which enables a deeper analysis. We further provide three exploratory analyses, detailing topic shares of different parties throughout time, a descriptive analysis of the development of the age of an average speaker as well as a sentiment analysis of speeches of different parties with regards to the COVID-19 pandemic.

cs.CL↗

arXiv2024

Zeitenwenden: Detecting changes in the German political discourse

From a monarchy to a democracy, to a dictatorship and back to a democracy -- the German political landscape has been constantly changing ever since the first German national state was formed in 1871. After World War II, the Federal Republic of Germany was formed in 1949. Since then every plenary session of the German Bundestag was logged and even has been digitized over the course of the last few years. We analyze these texts using a time series variant of the topic model LDA to investigate which events had a lasting effect on the political discourse and how the political topics changed over time. This allows us to detect changes in word frequency (and thus key discussion points) in political discourse.

cs.CL↗

arXiv2024

Lex2Sent: A bagging approach to unsupervised sentiment analysis

Unsupervised text classification, with its most common form being sentiment analysis, used to be performed by counting words in a text that were stored in a lexicon, which assigns each word to one class or as a neutral word. In recent years, these lexicon-based methods fell out of favor and were replaced by computationally demanding fine-tuning techniques for encoder-only models such as BERT and zero-shot classification using decoder-only models such as GPT-4. In this paper, we propose an alternative approach: Lex2Sent, which provides improvement over classic lexicon methods but does not require any GPU or external hardware. To classify texts, we train embedding models to determine the distances between document embeddings and the embeddings of the parts of a suitable lexicon. We employ resampling, which results in a bagging effect, boosting the performance of the classification. We show that our model outperforms lexica and provides a basis for a high performing few-shot fine-tuning approach in the task of binary sentiment analysis.

cs.CL↗

arXiv2024

Semi-parametric goodness-of-fit testing for INAR models

Among the various models designed for dependent count data, integer-valued autoregressive (INAR) processes enjoy great popularity. Typically, statistical inference for INAR models uses asymptotic theory that relies on rather stringent (parametric) assumptions on the innovations such as Poisson or negative binomial distributions. In this paper, we present a novel semi-parametric goodness-of-fit test tailored for the INAR model class. Relying on the INAR-specific shape of the joint probability generating function, our approach allows for model validation of INAR models without specifying the (family of the) innovation distribution. We derive the limiting null distribution of our proposed test statistic, prove consistency under fixed alternatives and discuss its asymptotic behavior under local alternatives. By manifold Monte Carlo simulations, we illustrate the overall good performance of our testing procedure in terms of power and size properties. In particular, it turns out that the power can be considerably improved by using higher-order test statistics. We conclude the article with the application on three real-world economic data sets.

stat.ME↗

arXiv2024

AR-Sieve Bootstrap for the Random Forest and a simulation-based comparison with rangerts time series prediction

The Random Forest (RF) algorithm can be applied to a broad spectrum of problems, including time series prediction. However, neither the classical IID (Independent and Identically distributed) bootstrap nor block bootstrapping strategies (as implemented in rangerts) completely account for the nature of the Data Generating Process (DGP) while resampling the observations. We propose the combination of RF with a residual bootstrapping technique where we replace the IID bootstrap with the AR-Sieve Bootstrap (ARSB), which assumes the DGP to be an autoregressive process. To assess the new model's predictive performance, we conduct a simulation study using synthetic data generated from different types of DGPs. It turns out that ARSB provides more variation amongst the trees in the forest. Moreover, RF with ARSB shows greater accuracy compared to RF with other bootstrap strategies. However, these improvements are achieved at some efficiency costs.

stat.ML↗

arXiv2024

spINAR: An R Package for Semiparametric and Parametric Estimation and Bootstrapping of Integer-Valued Autoregressive (INAR) Models

Although the statistical literature extensively covers continuous-valued time series processes and their parametric, non-parametric and semiparametric estimation, the literature on count data time series is considerably less advanced. Among the count data time series models, the integer-valued autoregressive (INAR) model is arguably the most popular one finding applications in a wide variety of fields such as medical sciences, environmentology and economics. While many contributions have been made during the last decades, the majority of the literature focuses on parametric INAR models and estimation techniques. Our emphasis is on the complex but efficient and non-restrictive semiparametric estimation of INAR models. The appeal of this approach lies in the absence of a commitment to a parametric family of innovation distributions. In this paper, we describe the need and the features of our R package spINAR which combines semiparametric simulation, estimation and bootstrapping of INAR models also covering its parametric versions.

stat.CO↗

arXiv2023

Unsupervised Movement Detection in Indoor Positioning Systems of Production Halls

Consider indoor positioning systems (IPS) in production halls where objects equipped with sensors send their current position. Beside its large volume, the analyzation of the resulting raw data is challenging due to the susceptibility towards noise. Reasons are accuracy issues and undesired awakenings of sensors that occur due to the dynamics of logistic processes (e.g.~vibrations of passing forklifts). We propose a tailor-made statistical procedure for these challenges and combine visual analytics with movement detection. Contrary to common stay-point algorithms, we do not only distinguish between stops and moves, but also consider undesired awakenings. This leads to a more detailed interpretation scheme offering usages for online (e.g.~monitoring of orders) and offline applications (e.g.~detection of problematic areas). The approach does not require other information than the raw IPS output and enables an ad-hoc analysis. We underline our findings in an extensive case study with real IPS data of our industry partner.

cs.LG↗

arXiv2023

Goodness of fit testing based on graph functionals for homogenous Erdös Renyi graphs

The Erdös Renyi graph is a popular choice to model network data as it is parsimoniously parametrized, straightforward to interprete and easy to estimate. However, it has limited suitability in practice, since it often fails to capture crucial characteristics of real-world networks. To check the adequacy of this model, we propose a novel class of goodness-of-fit tests for homogeneous Erdös Renyi models against heterogeneous alternatives that allow for nonconstant edge probabilities. We allow for asymptotically dense and sparse networks. The tests are based on graph functionals that cover a broad class of network statistics for which we derive limiting distributions in a unified manner. The resulting class of asymptotic tests includes several existing tests as special cases. Further, we propose a parametric bootstrap and prove its consistency, which allows for performance improvements particularly for small network sizes and avoids the often tedious variance estimation for asymptotic tests. Moreover, we analyse the sensitivity of different goodness-of-fit test statistics that rely on popular choices of subgraphs. We evaluate the proposed class of tests and illustrate our theoretical findings by extensive simulations.

stat.ME↗

arXiv2023

Prototypes as Explanation for Time Series Anomaly Detection

Detecting abnormal patterns that deviate from a certain regular repeating pattern in time series is essential in many big data applications. However, the lack of labels, the dynamic nature of time series data, and unforeseeable abnormal behaviors make the detection process challenging. Despite the success of recent deep anomaly detection approaches, the mystical mechanisms in such black-box models have become a new challenge in safety-critical applications. The lack of model transparency and prediction reliability hinders further breakthroughs in such domains. This paper proposes ProtoAD, using prototypes as the example-based explanation for the state of regular patterns during anomaly detection. Without significant impact on the detection performance, prototypes shed light on the deep black-box models and provide intuitive understanding for domain experts and stakeholders. We extend the widely used prototype learning in classification problems into anomaly detection. By visualizing both the latent space and input space prototypes, we intuitively demonstrate how regular data are modeled and why specific patterns are considered abnormal.

cs.LG↗

arXiv2023

Bootstrap Consistency for the Mack Bootstrap

Mack's distribution-free chain ladder reserving model belongs to the most popular approaches in non-life insurance mathematics. Proposed to determine the first two moments of the reserve, it does not allow to identify the whole distribution of the reserve. For this purpose, Mack's model is usually equipped with a tailor-made bootstrap procedure. Although widely used in practice to estimate the reserve risk, no theoretical bootstrap consistency results exist that justify this approach. To fill this gap in the literature, we adopt the framework proposed by Steinmetz and Jentsch (2022) to derive asymptotic theory in Mack's model. By splitting the reserve into two parts corresponding to process and estimation uncertainty, this enables - for the first time - a rigorous investigation also of the validity of the Mack bootstrap. We prove that the (conditional) distribution of the asymptotically dominating process uncertainty part is correctly mimicked by Mack's bootstrap if the parametric family of distributions of the individual development factors is correctly specified. Otherwise, this is not the case. In contrast, the (conditional) distribution of the estimation uncertainty part is generally not correctly captured by Mack's bootstrap. To tackle this, we propose an alternative Mack-type bootstrap, which is designed to capture also the distribution of the estimation uncertainty part. We illustrate our findings by simulations and show that the newly proposed alternative Mack bootstrap performs superior to the Mack bootstrap.

math.ST↗