Austrian Journal of Statistics

Visualization of Record Swapping

Jiří Novák, Jaroslav Sixta — Tue, 16 Jan 2024 00:00:00 +0000

Record Swapping is a statistical disclosure control technique widely used to secure the confidentiality of microdata obtained in surveys and censuses. It is one of the methods recommended by the Centre of Excellence on Statistical Disclosure Control of the European Union for the protection of data from Census 2021. This method is based on the swapping of risk records between geographical areas. The analysis of perturbed microdata is usually done purely on numerical results, and only simplified schemes are used for general illustration. We wanted a comprehensive visualization, and therefore, we have prepared a~ visualization of record swapping based on Choropleth maps and Commuting Flow maps, also known as Origin-Destination maps. Choropleth maps use differing colours within predefined geographic areas to represent aggregated statistical data. Origin-Destination maps are widely used for visualization and a description of people commuting to work, but they can also be used to describe other indicators. We utilize these methods to visualize the swapping of records for individual statistical units (persons). This approach is demonstrated using microdata from the Population Census 2011 from the Czech Republic and synthetic Austrian EU-SILC data. The proposed visualization allows statistical offices and agencies to effectively evaluate the swapping process and the distribution of the records across geographical areas.

An Efficient Variant of Ranked Set Sampling, Probability Proportional to Size with Application to Economic Data

Saeid Amiri, Hossein Hassani, Saeed Heravi — Tue, 16 Jan 2024 00:00:00 +0000

In this paper, we apply the Ranked Set Sampling (RSS) technique to economic data in the form of homescan market research data set for the meat food group. The RSS method is then extended to select sampling units based on the Probability-Proportional-to-Size (PPS) approach. The new proposed ranked set sampling, using the PPS-derived method, RPPS, is assessed via Monte Carlo investigations and an extensive homescan data set to evaluate its performances. The results are promising and in line with theoretical and simulation studies, showing that the RPPS technique is more reliable and has a smaller variance than the PPS route.

Compound Conway-Maxwell Poisson Gamma Distribution: Properties and Estimation

Jahnavi Merupula, V S Vaidyanathan — Tue, 16 Jan 2024 00:00:00 +0000

The distribution of a random sum of random events is called a compound distribution. It involves a counting (discrete) distribution to model the number of occurrences of the random event in a fixed time period and a continuous distribution to model the outcome of the random event. It has applications in the fields of actuarial sciences, meteorology etc. For example, in modelling insurance loss amounts through compound distributions, the number of claims and the claim amounts are used to calculate the total claim amount of a portfolio. The number of claims is modelled through a discrete distribution and the claim amounts are modelled through continuous distributions. Generally, Poisson distribution is used in compound models as the discrete distribution and such models are known as compound Poisson models. However, the equi-dispersion property of the Poisson distribution hinders its application in scenarios where the underlying count data is either over- or under-dispersed. In this paper, a two-parameter Poisson distribution, namely, Conway-Maxwell Poisson (CMP) distribution, which handles both over- and under-dispersed data, is considered as the counting distribution, and the corresponding compound CMP distribution is developed. Some mathematical properties of the distribution are derived and a methodology to estimate the parameters using the likelihood approach is proposed. A numerical illustration of the proposed methodology is given through a simulation study. An application of the compound CMP model is illustrated through transportation security administration (TSA) insurance claim data. Also, the estimation of the risk measures associated with the TSA claim data is discussed.

Spatial Blind Source Separation in the Presence of a Drift

Christoph Muehlmann, Peter Filzmoser, Klaus Nordhausen — Tue, 16 Jan 2024 00:00:00 +0000

Multivariate measurements taken at different spatial locations occur frequently in practice. Proper analysis of such data needs to consider not only dependencies on-sight but also dependencies in and in-between variables as a function of spatial separation. Spatial Blind Source Separation (SBSS) is a recently developed unsupervised statistical tool that deals with such data by assuming that the observable data is formed by a linear latent variable model. In SBSS the latent variable is assumed to be constituted by weakly stationary random fields which are uncorrelated. Such a model is appealing as further analysis can be carried out on the marginal distributions of the latent variables, interpretations are straightforward as the model is assumed to be linear, and not all components of the latent field might be of interest which acts as a form of dimension reduction. The weakly stationarity assumption of SBSS implies that the mean of the data is constant for all sample locations, which might be too restricting in practical applications. Therefore, an adaptation of SBSS that uses scatter matrices based on differences was recently suggested in the literature. In our contribution we formalize these ideas, suggest a novel adapted SBSS method and show its usefulness on synthetic data and illustrate its use in a real data application.

On Diagnostics in Bell--Touchard Regression Models

Artur Lemonte — Tue, 16 Jan 2024 00:00:00 +0000

The Bell--Touchard regression model for count response variables was introduced recently in the statistical literature. This regression model for counts is, in some aspects, similar to the generalized linear model framework, and the mean response is related to covariates and unknown regression coefficients, which allows for parameter interpretation in terms of the response variable in its original scale. However, diagnostic methods for this class of regression models were not developed. In this paper, we fill this gap and propose a variety of diagnostic tools, such as leverage measures, global influence, normal curvatures of local influence under some perturbation schemes, and Pearson residuals. All diagnostic measures developed are applied in a real data set to analyze the fitted Bell--Touchard regression model in practice.

Forecasting Time-varying Value--at--Risk and Expected Shortfall Dependence: A Markov-switching Generalized Autoregressive Score Copula Approach

Katleho Makatjane — Tue, 16 Jan 2024 00:00:00 +0000

The importance of accurately forecasting extreme financial losses and their effects on the institutions involved in a given financial market has been highlighted by recent financial catastrophes. The flexibility with which econometric models can take into account the highly non-linear and asymmetric dependence in financial returns is a critical component of their capacity to forecast extreme events. Therefore, this study aims to forecast time-varying Value-at-Risk and expected shortfall dependence as a predictive density-based regime changes over time. To achieve this, a non-stationary Markov-switching generalized Autoregressive score model nested with copula is estimated using expectation–maximization (EM) algorithm. Extending this non-stationary model is quite challenging, as it requires specifications not only on how the usual parameters change over time but also those with mass distribution components. Dynamics of the estimated autoregressive score allowed the copula parameters to respond rapidly to time-varying key systemic parameters and risk. This is because regime changes are allowed to oscillated between high and low regimes. This is a clear indication of a regime shift in the parameters of an estimated model. Using the minimum score combining, six extreme value distributions are combined to the estimated MS(2)-GAS(1)-copula model and assessed the performance of each combined model 5 days and 30 days forecasting of value-at-risk and expected shortfall. The results of the forecasting performance indicated that the MS(2)-GAS(1)-GPD is the best model to model and forecast Value-at-risk and expected shortfall for the Botswana stock market. This is a promising technique for stochastic modeling of time-varying Value-at-Risk and Expected Shortfall. In addition, a foundation is provided for future researchers to conduct studies on emerging markets. These results are also important for risk managers and investors.

Generalized Sum-Asymmetry Model and Orthogonality of Test Statistic for Square Contingency Tables

Shuji Ando — Tue, 16 Jan 2024 00:00:00 +0000

For analyzing contingency tables, we are usually interested in whether or not the independence model holds. On the other hand, for the analysis of square contingency tables, we are usually interested in whether or not the model having the structure of symmetry or asymmetry with respect to the main diagonals cells holds. This study proposes a generalized sum-asymmetry model including the exponential and relative exponential sum-symmetry models. This generalized model indicates that the cumulative probability that the sum of classes for row and column variables is s within the upper right cell of the table, is exponentially higher than the cumulative probability that the sum of classes for row and column variables is s within the lower left cell. Additionally, this study gives a separation of the sum-symmetry model using the proposed model, and reveals that the new separation satisfies the asymptotic equivalence for the test statistic. The utilities of the proposed methods are demonstrated through the real data analysis.

Dr. Hannes Ledolter (1950-2023): Obituary

Peter Hackl — Tue, 16 Jan 2024 00:00:00 +0000

Obituary for Hannes Ledolter