arXiv subjects

Andrej Srakar

Publications and source records attributed to Andrej Srakar.

3 recordsLinked to original sources

arXiv2025

Short survey of results and open problems for parking problems on random trees

Parking problems derive from works in combinatorics by Konheim and Weiss in the 1960s. In a memorable contribution, Lackner and Panholzer (2016) studied parking on a random tree and established a phase transition for this process when \(m \approx \frac{n}{2}\). This relates to the renowned result by David Aldous of convergence results on Erdős-Renyi random graphs of order \(n^{\frac{2}{3}}\). In a series of recent articles, Contat and coauthors have studied the problem in various random tree contexts and derived several novel scaling limit and phase transition results. We survey the present state-of-the-art of this literature and point to its extensions, open directions and possibilities, in particular related to the study of problem in different metric topologies. My intent it to point to importance of this line of research and novel open problems for future study.

math.PR↗

arXiv2020

MIMIC modelling with instrumental variables: A 2SLS-MIMIC approach

Multiple Indicators Multiple Causes (MIMIC) models are type of structural equation models, a theory-based approach to confirm the influence of a set of exogenous causal variables on the latent variable, and also the effect of the latent variable on observed indicator variables. In a common MIMIC model, multiple indicators reflect the underlying latent variables/factors, and the multiple causes (observed predictors) affect latent variables/factors. Basic assumptions of MIMIC are clearly violated in case of a variable being both an indicator and a cause, i.e. in the presence of reverse causality. Furthermore, the model is then unidentified. To resolve the situation, which can arise frequently, and as MIMIC estimation lacks closed form solutions for parameters we utilize a version of Bollen's (1996) 2SLS estimator for structural equation models combined with Jöreskog (1970)'s method of the analysis of covariance structures to derive a new, 2SLS estimator for MIMIC models. Our 2SLS empirical estimation is based on static MIMIC specification but we point also to dynamic/error-correction MIMIC specification and 2SLS solution for it. We derive basic asymptotic theory for static 2SLS-MIMIC, present a simulation study and apply findings to an interesting empirical case of estimating precarious status of older workers (using dataset of Survey of Health, Ageing and Retirement in Europe) which solves an important issue of the definition of precarious work as a multidimensional concept, not modelled adequately so far.

stat.AP↗

arXiv2020

New clustering approach for symbolic polygonal data: application to the clustering of entrepreneurial regimes

Entrepreneurial regimes are topic, receiving ever more research attention. Existing studies on entrepreneurial regimes mainly use common methods from multivariate analysis and some type of institutional related analysis. In our analysis, the entrepreneurial regimes is analyzed by applying a novel polygonal symbolic data cluster analysis approach. Considering the diversity of data structures in Symbolic Data Analysis (SDA), interval-valued data is the most popular. Yet, this approach requires assuming equidistribution hypothesis. We use a novel polygonal cluster analysis approach to address this limitation with additional advantages: to store more information, to significantly reduce large data sets preserving the classical variability through polygon radius, and to open new possibilities in symbolic data analysis. We construct a dynamic cluster analysis algorithm for this type of data with proving main theorems and lemmata to justify its usage. In the empirical part we use dataset of Global Entrepreneurship Monitor (GEM) for year 2015 to construct typologies of countries based on responses to main entrepreneurial questions. The article presents a novel approach to clustering in statistical theory (with novel type of variables never accounted for) and application to a pressing issue in entrepreneurship with novel results.

stat.ME↗