arXiv subjects

Ričardas Zitikis

Publications and source records attributed to Ričardas Zitikis.

16 recordsLinked to original sources

arXiv2025

Performance of diverse evaluation metrics in NLP-based assessment and text generation of consumer complaints

Machine learning (ML) has significantly advanced text classification by enabling automated understanding and categorization of complex, unstructured textual data. However, accurately capturing nuanced linguistic patterns and contextual variations inherent in natural language, particularly within consumer complaints, remains a challenge. This study addresses these issues by incorporating human-experience-trained algorithms that effectively recognize subtle semantic differences crucial for assessing consumer relief eligibility. Furthermore, we propose integrating synthetic data generation methods that utilize expert evaluations of generative adversarial networks and are refined through expert annotations. By combining expert-trained classifiers with high-quality synthetic data, our research seeks to significantly enhance machine learning classifier performance, reduce dataset acquisition costs, and improve overall evaluation metrics and robustness in text classification tasks.

cs.CL↗

arXiv2025

Fundamentals of non-parametric statistical inference for integrated quantiles

We present a general non-parametric statistical inference theory for integrals of quantiles without assuming any specific sampling design or dependence structure. Technical considerations are accompanied by examples and discussions, including those pertaining to the bias of empirical estimators. To illustrate how the general results can be adapted to specific situations, we derive - at a stroke and under minimal conditions - consistency and asymptotic normality of the empirical tail-value-at-risk, Lorenz and Gini curves at any probability level in the case of the simple random sampling, thus facilitating a comparison of our results with what is already known in the literature. Results, notes and references concerning dependent (i.e., time series) data are also offered. As a by-product, our general results provide new and unified proofs of large-sample properties of a number of classical statistical estimators, such as trimmed means, and give additional insights into the origins of, and the reasons for, various necessary and sufficient conditions.

math.ST↗

arXiv2024

NLP-based detection of systematic anomalies among the narratives of consumer complaints

We develop an NLP-based procedure for detecting systematic nonmeritorious consumer complaints, simply called systematic anomalies, among complaint narratives. While classification algorithms are used to detect pronounced anomalies, in the case of smaller and frequent systematic anomalies, the algorithms may falter due to a variety of reasons, including technical ones as well as natural limitations of human analysts. Therefore, as the next step after classification, we convert the complaint narratives into quantitative data, which are then analyzed using an algorithm for detecting systematic anomalies. We illustrate the entire procedure using complaint narratives from the Consumer Complaint Database of the Consumer Financial Protection Bureau.

stat.ME↗

arXiv2022

Tail maximal dependence in bivariate models: estimation and applications

Assessing dependence within co-movements of financial instruments has been of much interest in risk management. Typically, indices of tail dependence are used to quantify the strength of such dependence, although many of the indices underestimate the strength. Hence, we advocate the use of a statistical procedure designed to estimate the maximal strength of dependence that can possibly occur among the co-movements. We illustrate the procedure using simulated and real data-sets.

stat.ME↗

arXiv2022

Detecting systematic anomalies affecting systems when inputs are stationary time series

We develop an anomaly-detection method when systematic anomalies, possibly statistically very similar to genuine inputs, are affecting control systems at the input and/or output stages. The method allows anomaly-free inputs (i.e., those before contamination) to originate from a wide class of random sequences, thus opening up possibilities for diverse applications. To illustrate how the method works on data, and how to interpret its results and make decisions, we analyze several actual time series, which are originally non-stationary but in the process of analysis are converted into stationary. As a further illustration, we provide a controlled experiment with anomaly-free inputs following an ARMA time series model under various contamination scenarios.

stat.ME↗

arXiv2020

Functional Correlations in the Pursuit of Performance Assessment of Classifiers

In statistical classification and machine learning, as well as in social and other sciences, a number of measures of association have been proposed for assessing and comparing individual classifiers, raters, as well as their groups. In this paper, we introduce, justify, and explore several new measures of association, which we call CO-, ANTI- and COANTI-correlation coefficients, that we demonstrate to be powerful tools for classifying confusion matrices. We illustrate the performance of these new coefficients using a number of examples, from which we also conclude that the coefficients are new objects in the sense that they differ from those already in the literature.

stat.ML↗

arXiv2018

Searching for, and quantifying, non-convexity of functions

Convexity plays a prominent role in a number of problems, but practical considerations frequently give rise to non-convex functions. We suggest a method for determining convex regions, and also for assessing the lack of convexity in the other regions. The method relies on a specially constructed decomposition of symmetric matrices, such as the Hessian. We illustrate theoretical results using several examples, one of which analyses a problem arising in risk measurement and management in insurance and finance.

math.FA↗

arXiv2018

Assessing transfer functions in control systems

When dealing with control systems, it is useful and even necessary to assess the performance of underlying transfer functions. The functions may or may not be linear, may or may not be even monotonic. In addition, they may have structural breaks and other abberations that require monitoring and quantification to aid decision making. The present paper develops such a methodology, which is based on an index of increase that naturally arises as the solution to an optimization problem. We show theoretically and illustrate numerically that the empirical counterpart of the index needs to be used with great care and in-depth knowledge of the problem at hand in order to achieve desired large-sample properties, such as consistency.

math.ST↗

arXiv2018

Detecting intrusions in control systems: a rule of thumb, its justification and illustrations

Control systems are exposed to unintentional errors, deliberate intrusions, false data injection attacks, and various other disruptions. In this paper we propose, justify, and illustrate a rule of thumb for detecting, or confirming the absence of, such disruptions. To facilitate the use of the rule, we rigorously discuss background results that delineate the boundaries of the rule's applicability. We also discuss ways to further widen the applicability of the proposed intrusion-detection methodology.

stat.ME↗

arXiv2018

Estimating the index of increase via balancing deterministic and random data

We introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement-errors. We prove consistency of the index and show how its rate of convergence is influenced by deterministic and random parts of the data. In particular, the obtained results suggest a frequency at which observations should be taken in order to reach any pre-specified level of estimation precision. We illustrate the index using data arising from purely deterministic and error-contaminated functions, which may or may not be monotonic.

math.ST↗

arXiv2017

Quantifying non-monotonicity of functions and the lack of positivity in signed measures

In various research areas related to decision making, problems and their solutions frequently rely on certain functions being monotonic. In the case of non-monotonic functions, one would then wish to quantify their lack of monotonicity. In this paper we develop a method designed specifically for this task, including quantification of the lack of positivity, negativity, or sign-constancy in signed measures. We note relevant applications in Insurance, Finance, and Economics, and discuss some of them in detail.

math.PR↗

arXiv2017

Weighted allocations, their concomitant-based estimators, and asymptotics

Various members of the class of weighted insurance premiums and risk capital allocation rules have been researched from a number of perspectives. Corresponding formulas in the case of parametric families of distributions have been derived, and they have played a pivotal role when establishing parametric statistical inference in the area. Non-parametric inference results have also been derived in special cases such as the tail conditional expectation, distortion risk measure, and several members of the class of weighted premiums. For weighted allocation rules, however, non-parametric inference results have not yet been adequately developed. In the present paper, therefore, we put forward empirical estimators for the weighted allocation rules and establish their consistency and asymptotic normality under practically sound conditions. Intricate statistical considerations rely on the theory of induced order statistics, known as concomitants.

math.ST↗

arXiv2017

Statistical foundations for assessing the difference between the classical and weighted-Gini betas

The `beta' is one of the key quantities in the capital asset pricing model (CAPM). In statistical language, the beta can be viewed as the slope of the regression line fitted to financial returns on the market against the returns on the asset under consideration. The insurance counterpart of CAPM, called the weighted insurance pricing model (WIPM), gives rise to the so-called weighted-Gini beta. The aforementioned two betas may or may not coincide, depending on the form of the underlying regression function, and this has profound implications when designing portfolios and allocating risk capital. To facilitate these tasks, in this paper we develop large-sample statistical inference results that, in a straightforward fashion, imply confidence intervals for, and hypothesis tests about, the equality of the two betas.

math.ST↗

arXiv2016

Paths and indices of maximal tail dependence

We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the context of both symmetric and asymmetric copulas with and without singularities. As a remedy, we introduce a notion of paths of maximal (tail) dependence and utilize it to propose several new indices of tail dependence. The suggested new indices are conservative, conform with the basic concepts of modern quantitative risk management, and are able to distinguish between distinct risky positions in situations when the existing indices fail to do so.

math.PR↗

arXiv2011

Coupled risk measures and their empirical estimation when losses follow heavy-tailed distributions

Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a number of risk measures that are of the form of ratios, or even more complex combinations, of two L-functionals. In the present paper we call such combinations `coupled risk measures' and develop a statistical inferential theory for them when losses follow heavy-tailed distributions. Our theory implies -at a stroke- statistical inferential results for absolute and relative distortion risk measures, weighted premium calculation principles, as well as for many indices of economic inequality that have appeared in the econometric literature.

math.ST↗

arXiv2011

Aggregate claims when their sizes and arrival times are dependent and governed by a general point process

We suggest a general method for analyzing aggregate insurance claims that arrive according to a very general point process, known in the literature as the order statistic point process, which includes as special cases the classical compound Poisson and the Sparre Andersen models, among many others. We also allow for the process to govern claim sizes via a general dependence structure that relates claim sizes to claim and/or inter-claim times. The obtained general results are supplemented with special closed-form illustrative formulas, that also exemplify the potential for future research in the area.

math.PR↗