arXiv subjects

Dimitris Karlis

Publications and source records attributed to Dimitris Karlis.

At least 19 recordsLinked to original sources

arXiv2026

Beyond Equidistant Assumptions: An Autoregressive Ordered Stereotype Model for Ordinal Time Series

We propose an extension of the ordered stereotype model (OSM) for ordinal time series data, referred to as the Autoregressive OSM (AR-OSM). The model captures serial dependence by incorporating lagged values of the response as covariates in the systematic component. In contrast to existing regression models for ordinal time series, the AR-OSM does not assume equidistant categories, but instead allows the data to determine their relative spacing. This property makes the model particularly suitable for applications where the equidistance assumption is unrealistic. Such a case is illustrated through the analysis of infant sleep state data. Additionally, a comprehensive simulation study is conducted to assess the performance of the model under varying sample sizes and to investigate how parameter values influence the induced serial dependence structure.

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arXiv2026

Modelling multivariate ordinal time series using pairwise likelihood

We assume that we have multiple ordinal time series and we would like to specify their joint distribution. In general it is difficult to create multivariate distribution that can be easily used to jointly model ordinal variables and the problem becomes even more complex in the case of time series, since we have to take into consideration not only the autocorrelation of each time series and the dependence between time series, but also cross-correlation. Starting from the simplest case of two ordinal time series, we propose using copulas to specify their joint distribution. We extend our approach in higher dimensions, by approximating full likelihood with composite likelihood and especially conditional pairwise likelihood, where each bivariate model is specified by copulas. We suggest maximizing each bivariate model independently to avoid computational issues and synthesize individual estimates using weighted mean. Weights are related to the Hessian matrix of each bivariate model. Simulation studies showed that model fits well under different sample sizes. Forecasting approach is also discussed. A small real data application about unemployment state of different countries of European Union is presented to illustrate our approach.

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arXiv2025

Maximum Likelihood Estimation of the Vector AutoRegressive To Anything (VARTA) model

The literature on multivariate time series is, largely, limited to either models based on the multivariate Gaussian distribution or models specifically developed for a given application. In this paper we develop a general approach which is based on an underlying, unobserved, Gaussian Vector Autoregressive (VAR) model. Using a transformation, we can capture the time dynamics as well as the distributional properties of a multivariate time series. The model is called the Vector AutoRegressive To Anyting (VARTA) model and was originally presented by Biller and Nelson (2003) who used it for the purpose of simulation. In this paper we derive a maximum likelihood estimator for the model and investigate its performance. We also provide diagnostic analysis and how to compute the predictive distribution. The proposed approach can provide better estimates about the forecasting distributions which can be of every kind not necessarily Gaussian distributions as for the standard VAR models.

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arXiv2025

A Bivariate DAR($1$) model for ordinal time series

We present a bivariate vector valued discrete autoregressive model of order $1$ (BDAR($1$)) for discrete time series. The BDAR($1$) model assumes that each time series follows its own univariate DAR($1$) model with dependent random mechanisms that determine from which component the current status occurs and dependent innovations. The joint distribution of the random mechanisms which are expressed by Bernoulli vectors are proposed to be defined through copulas. The same holds for the joint distribution of innovation terms. Properties of the model are provided, while special focus is given to the case of bivariate ordinal time series. A simulation study is presented, indicating that model provides efficient estimates even in case of moderate sample size. Finally, a real data application on unemployment state of two countries is presented, for illustrating the proposed model.

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arXiv2024

Efficient subsampling for high-dimensional data

In the field of big data analytics, the search for efficient subdata selection methods that enable robust statistical inferences with minimal computational resources is of high importance. A procedure prior to subdata selection could perform variable selection, as only a subset of a large number of variables is active. We propose an approach when both the size of the full dataset and the number of variables are large. This approach firstly identifies the active variables by applying a procedure inspired by random LASSO (Least Absolute Shrinkage and Selection Operator) and then selects subdata based on leverage scores to build a predictive model. Our proposed approach outperforms approaches that already exists in the current literature, including the usage of the full dataset, in both variable selection and prediction, while also exhibiting significant improvements in computing time. Simulation experiments as well as a real data application are provided.

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arXiv2024

A Model-Based Approach to Shot Charts Estimation in Basketball

Shot charts in basketball analytics provide an indispensable tool for evaluating players' shooting performance by visually representing the distribution of field goal attempts across different court locations. However, conventional methods often overlook the bounded nature of the basketball court, leading to inaccurate representations, particularly along the boundaries and corners. In this paper, we propose a novel model-based approach to shot chart estimation and visualization that explicitly considers the physical boundaries of the basketball court. By employing Gaussian mixtures for bounded data, our methodology allows to obtain more accurate estimation of shot density distributions for both made and missed shots. Bayes' rule is then applied to derive estimates for the probability of successful shooting from any given locations, and to identify the regions with the highest expected scores. To illustrate the efficacy of our proposal, we apply it to data from the 2022-23 NBA regular season, showing its usefulness through detailed analyses of shot patterns for two prominent players.

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arXiv2024

On the estimation of complex statistics combining different surveys

The importance of exploring a potential integration among surveys has been acknowledged in order to enhance effectiveness and minimize expenses. In this work, we employ the alignment method to combine information from two different surveys for the estimation of complex statistics. The derivation of the alignment weights poses challenges in case of complex statistics due to their non-linear form. To overcome this, we propose to use a linearized variable associated with the complex statistic under consideration. Linearized variables have been widely used to derive variance estimates, thus allowing for the estimation of the variance of the combined complex statistics estimates. Simulations conducted show the effectiveness of the proposed approach, resulting to the reduction of the variance of the combined complex statistics estimates. Also, in some cases, the usage of the alignment weights derived using the linearized variable associated with a complex statistic, could result in a further reduction of the variance of the combined estimates.

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arXiv2024

Modelling handball outcomes using univariate and bivariate approaches

Handball has received growing interest during the last years, including academic research for many different aspects of the sport. On the other hand modelling the outcome of the game has attracted less interest mainly because of the additional challenges that occur. Data analysis has revealed that the number of goals scored by each team are under-dispersed relative to a Poisson distribution and hence new models are needed for this purpose. Here we propose to circumvent the problem by modelling the score difference. This removes the need for special models since typical models for integer data like the Skellam distribution can provide sufficient fit and thus reveal some of the characteristics of the game. In the present paper we propose some models starting from a Skellam regression model and also considering zero inflated versions as well as other discrete distributions in $\mathbb Z$. Furthermore, we develop some bivariate models using copulas to model the two halves of the game and thus providing insights on the game. Data from German Bundesliga are used to show the potential of the new models.

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arXiv2024

Multinomial mixture for spatial data

The purpose of this paper is to extend standard finite mixture models in the context of multinomial mixtures for spatial data, in order to cluster geographical units according to demographic characteristics. The spatial information is incorporated on the model through the mixing probabilities of each component. To be more specific, a Gibbs distribution is assumed for prior probabilities. In this way, assignment of each observation is affected by neighbors' cluster and spatial dependence is included in the model. Estimation is based on a modified EM algorithm which is enriched by an extra, initial step for approximating the field. The simulated field algorithm is used in this initial step. The presented model will be used for clustering municipalities of Attica with respect to age distribution of residents.

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arXiv2023

Extending the Dixon and Coles model: an application to women's football data

The prevalent model by Dixon and Coles (1997) extends the double Poisson model where two independent Poisson distributions model the number of goals scored by each team by moving probabilities between the scores 0-0, 0-1, 1-0, and 1-1. We show that this is a special case of a multiplicative model known as the Sarmanov family. Based on this family, we create more suitable models by moving probabilities between scores and employing other discrete distributions. We apply the new models to women's football scores, which exhibit some characteristics different than that of men's football.

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arXiv2023

Optimal subdata selection for linear model selection

If the assumed model does not accurately capture the underlying structure of the data, a statistical method is likely to yield sub-optimal results, and so model selection is crucial in order to conduct any statistical analysis. However, in case of massive datasets, the selection of an appropriate model from a large pool of candidates becomes computationally challenging, and limited research has been conducted on data selection for model selection. In this study, we conduct subdata selection based on the A-optimality criterion, allowing to perform model selection on a smaller subset of the data. We evaluate our approach based on the probability of selecting the best model and on the estimation efficiency through simulation experiments and two real data applications.

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arXiv2023

On the selection of optimal subdata for big data regression based on leverage scores

The demand of computational resources for the modeling process increases as the scale of the datasets does, since traditional approaches for regression involve inverting huge data matrices. The main problem relies on the large data size, and so a standard approach is subsampling that aims at obtaining the most informative portion of the big data. In the current paper, we explore an existing approach based on leverage scores, proposed for subdata selection in linear model discrimination. Our objective is to propose the aforementioned approach for selecting the most informative data points to estimate unknown parameters in both the first-order linear model and a model with interactions. We conclude that the approach based on leverage scores improves existing approaches, providing simulation experiments as well as a real data application.

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arXiv2023

Subdata selection for big data regression: an improved approach

In the big data era researchers face a series of problems. Even standard approaches/methodologies, like linear regression, can be difficult or problematic with huge volumes of data. Traditional approaches for regression in big datasets may suffer due to the large sample size, since they involve inverting huge data matrices or even because the data cannot fit to the memory. Proposed approaches are based on selecting representative subdata to run the regression. Existing approaches select the subdata using information criteria and/or properties from orthogonal arrays. In the present paper we improve existing algorithms providing a new algorithm that is based on D-optimality approach. We provide simulation evidence for its performance. Evidence about the parameters of the proposed algorithm is also provided in order to clarify the trade-offs between execution time and information gain. Real data applications are also provided.

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arXiv2021

Piecewise survival models: a change-point analysis on herpes zoster associated pain data revisited and extended

For many diseases it is reasonable to assume that the hazard rate is not constant across time, but also that it changes in different time intervals. To capture this, we work here with a piecewise survival model. One of the major problems in such piecewise models is to determine the time points of change of the hazard rate. From the practical point of view this can provide very important information as it may reflect changes in the progress of a disease. We present piecewise Weibull regression models with covariates. The time points where change occurs are assumed unknown and need to be estimated. The equality of hazard rates across the distinct phases is also examined to verify the exact number of phases. An example based on herpes zoster data has been used to demonstrate the usefulness of the developed methodology.

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arXiv2020

Bayesian inference for transportation origin-destination matrices: the Poisson-inverse Gaussian and other Poisson mixtures

In this paper we present Poisson mixture approaches for origin-destination (OD) modeling in transportation analysis. We introduce covariate-based models which incorporate different transport modeling phases and also allow for direct probabilistic inference on link traffic based on Bayesian predictions. Emphasis is placed on the Poisson-inverse Gaussian as an alternative to the commonly-used Poisson-gamma and Poisson-lognormal models. We present a first full Bayesian formulation and demonstrate that the Poisson-inverse Gaussian is particularly suited for OD analysis due to desirable marginal and hierarchical properties. In addition, the integrated nested Laplace approximation (INLA) is considered as an alternative to Markov chain Monte Carlo and the two methodologies are compared under specific modeling assumptions. The case study is based on 2001 Belgian census data and focuses on a large, sparsely-distributed OD matrix containing trip information for 308 Flemish municipalities.

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arXiv2020

Infinite mixtures of multivariate normal-inverse Gaussian distributions for clustering of skewed data

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework, either the number of components needs to be known $a$-$priori$ or needs to be estimated $a$-$posteriori$ using some model selection criterion after deriving results for a range of possible number of components. However, different model selection criteria can sometimes result in different number of components yielding uncertainty. Here, an infinite mixture model framework, also known as Dirichlet process mixture model, is proposed for the mixtures of MNIG distributions. This Dirichlet process mixture model approach allows the number of components to grow or decay freely from 1 to $\infty$ (in practice from 1 to $N$) and the number of components is inferred along with the parameter estimates in a Bayesian framework thus alleviating the need for model selection criteria. We provide real data applications with benchmark datasets as well as a small simulation experiment to compare with other existing models. The proposed method provides competitive clustering results to other clustering approaches for both simulation and real data and parameter recovery are illustrated using simulation studies.

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arXiv2020

A Bayesian approach for clustering skewed data using mixtures of multivariate normal-inverse Gaussian distributions

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented, based on the multivariate normal inverse Gaussian (MNIG) distribution. For parameter estimation of the mixture, a Bayesian approach via Gibbs sampler is used; for this, a novel approach to simulate univariate generalized inverse Gaussian random variables and matrix generalized inverse Gaussian random matrices is provided. The proposed algorithm will be applied to both simulated and real data. Through simulation studies and real data analysis, we show parameter recovery and that our approach provides competitive clustering results compared to other clustering approaches.

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arXiv2019

Clustering Discrete-Valued Time Series

There is a need for the development of models that are able to account for discreteness in data, along with its time series properties and correlation. Our focus falls on INteger-valued AutoRegressive (INAR) type models. The INAR type models can be used in conjunction with existing model-based clustering techniques to cluster discrete-valued time series data. With the use of a finite mixture model, several existing techniques such as the selection of the number of clusters, estimation using expectation-maximization and model selection are applicable. The proposed model is then demonstrated on real data to illustrate its clustering applications.

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