Austrian Journal of Statistics

Product Autoregressive Models: Review of Properties, Estimation Methods and Applications

Rahul Thekkedath, Shiji Kavungal, Muhammed Anvar P — Wed, 28 May 2025 00:00:00 +0000

Analysis of continuous non-negative time series data using multiplicative models is a growing area of research. When the variable of interest is non-negative, often some methodology based on transformation was followed in the literature. Even though a useful class of models known as product autoregressive models was appeared in the literature long back, the further advancements happened only in the last decade. Through subsequent developments, it was shown that the product form of an additive autoregressive model is preferable to its linear counterpart when non-negativity has to be taken care. This paper aims to provide an exhaustive review of theoretical and empirical works conducted on product autoregressive models in the context of non-linear and non-Gaussian time series modelling. The notable properties, estimation methods and applications of these models are discussed followed by a description of some possible future research avenues on this area.

On a Control Chart for Monitoring Rates and Proportions Based on the Standard Two-sided Power Distribution

Artur Lemonte — Wed, 28 May 2025 00:00:00 +0000

This paper proposes a new control chart based on the two-parameter standard two-sided power distribution for monitoring rates and proportions, that is, when the quality characteristic of interest belongs to the unit interval (0,1). Control charts based on the well-known beta and Kumaraswamy distributions are usually considered to deal with this kind of data. The standard two-sided power distribution
has many similarities to the beta and Kumaraswamy distributions and a number of advantages in terms of tractability. We evaluate and compare the performance of the new control chart with the beta and Kumaraswamy control charts through Monte Carlo simulation experiments. The simulation results reveal that the control chart based on the standard two-sided power distribution outperforms the beta and Kumaraswamy control charts in terms of run length analysis. An empirical application to a real data set is considered to
illustrate the new control chart in practice, and comparisons with the two most traditional control charts for rates and proportions (beta and Kumaraswamy) are made.

Excess Mortality in Austria during the COVID-19 Pandemic

Matthias Reitzner — Wed, 28 May 2025 00:00:00 +0000

The impact of the COVID-19 pandemic on the mortality in Austria is investigated. A recent pre-pandemic generation life table is developed. Using this pre-pandemic life table, the expected number of deaths for the years 2020 to 2023 is derived. Comparing the expected number of deaths to the observed number of deaths during the pandemic years yields the excess mortality for Austria in the years 2020 to 2023.

The Austrian life table can be adjusted to the Austrian federal states, yielding for each Austrian federal state the excess mortality for the pandemic years. The excess mortality varies substantially across federal states and during the pandemic years.

The results are discussed against some state-specific health-related and economic quantities, yielding correlations of excess mortality with age, medical care, economic quantities, and COVID-19 related quantities.

Stochastic Restricted Modified Mixed Logistic Estimator

Thayaparan Kayathiri, Manickavasagar Kayanan, Pushpakanthie Wijekoon — Wed, 28 May 2025 00:00:00 +0000

In this study, we introduce a new estimator named the Stochastic Restricted Modified Mixed Logistic Estimator (SRMMLE), which is specifically designed to handle multicollinearity within the framework of stochastic linear restrictions. Further, we enhance the SRMMLE by modifying its coefficients, resulting in four distinct variants: Stochastic Restricted Modified Mixed Logistic Estimator 1 (SRMMLE1), Stochastic Restricted Modified Mixed Logistic Estimator 2 (SRMMLE2), Stochastic Restricted Modified Mixed Logistic Estimator 3 (SRMMLE3), and Stochastic Restricted Modified Mixed Logistic Estimator 4 (SRMMLE4). Based on the mean square error matrix criterion, we establish conditions for the superiority of SRMMLE over existing estimators, such as the Stochastic Restricted Maximum Likelihood Estimator (SRMLE), Stochastic Restricted Ridge Maximum Likelihood Estimator (SRRMLE), Stochastic Restricted Logistic Liu Estimator (SRLLE), and Stochastic Restricted Mixed Liu-Type Estimator (SRMLTE). In the simulation study, we determined the scalar mean square error and the K-fold cross-validated balanced accuracy of the estimators. Further, we present an empirical study and a real data application illustrating the superior performance of the proposed estimator. In particular, the SRMMLE4 outperforms others in terms of scalar mean square error and balanced accuracy.

E-Bayesian Estimation of Rayleigh Distribution and Its Evaluation Standards: E-posterior Risks and E-MSEs under Progressive Type-II Censoring

Mahesh Kumar Panda, Lipsa Rani Bhoi — Wed, 28 May 2025 00:00:00 +0000

The present study considers the problem of estimating the scale parameter, reliability function, and hazard function of Rayleigh distribution using the E-Bayesian estimation approach when progressively Type-II censored data are available. The evaluation standards of these estimates are accessed through the definition of E-posterior risk (expected posterior risk) and E-MSE (expected mean square error). These estimations are carried out using conjugate prior distributions of the unknown parameters under four different loss functions i.e. quadratic, weighted squared error, Degroot, and entropy loss functions. Further, we perform Monte Carlo simulations to compare the performances of these proposed methods and use a real dataset for illustration purposes.

Inference on Partially Observed Competing Risks Models Using Generalized Type-II Hybrid Censoring Scheme

G. S. Deepthy, K. K. Anakha, Sebastian Nicy — Wed, 28 May 2025 00:00:00 +0000

This article investigates inference in a competing risks model where failure causes are partially observed, assuming latent failure times follow Weibull distributions. Inference is derived under a generalized type-II hybrid censoring scheme. The maximum likelihood estimators for model parameters and their associated confidence intervals are discussed. Also, we compute Bayes estimators under both informative and non-informative priors, along with their credible intervals. The performance of all estimators is evaluated through Monte Carlo simulations. Finally, for illustrative purposes, a real-world case is explored.

cellKey - An R Package to Perturb Statistical Tables

Bernhard Meindl — Wed, 28 May 2025 00:00:00 +0000

National statistical offices (NSIs) routinely publish aggregated data in the form of statistical tables. However, ensuring data privacy is a critical aspect of this process. Anonymization techniques must be applied to these tables to safeguard the privacy of individual data contributors and prevent unauthorized inference about specific units from the published outputs as often required by law. The R package cellKey offers a possible solution to this challenge by implementing a post-tabular perturbation method. This method modifies table cell values after aggregation, ensuring that sensitive information is adequately masked. It is versatile, suitable for both frequency tables and magnitude tables. A key feature of the cellKey package is its ability to maintain consistency across multiple tables that share identical cells. This ensures that anonymized data across different tables remains coherent while still protecting privacy. This approach makes the package especially useful for scenarios involving complex datasets with interrelated tables. The cellKey package is user-friendly and can empower NSIs and other data holders to publish statistical outputs that uphold both data utility and privacy, meeting the growing demands for secure and accessible data dissemination.