arXiv subjects

Piotr Chlebicki

Publications and source records attributed to Piotr Chlebicki.

5 recordsLinked to original sources

arXiv2025

Splitting infinity: a de Finetti game with state-dependent profit rates and singular control for diffusions

We study a game of resource extraction of a common good under one-dimensional diffusive dynamics with player actions corresponding to singular stochastic control up to absorption at $0$, implying a trade-off between profitable resource extraction and sustainability. Unsurprisingly, immediate extraction of all available resources is an equilibrium. A main result is that we characterize and prove the existence of non-trivial equilibria that do not result in immediate absorption, but instead are attained with both players extracting resources according to a state-dependent rate of threshold type, corresponding to the presence of control only when the state process is in an interval $(b,\infty)$. The underlying assumption is, roughly, that the drift coefficient of the uncontrolled state process grows sufficiently fast in relation to the discount rate, implying that the value for the corresponding one-player problem is infinite. We also study a generalization of the game that allows a state-dependent profit rate integrated against the control processes. In this game we again characterize and prove the existence of non-trivial equilibria of threshold type. In particular, a main novelty is that we find equilibria where the state process is controlled with its own local time such that we have reflection points with associated initial jumps, as well as other points in the state space where the control processes increase in a singular manner (skew points).

math.PR↗

arXiv2025

nonprobsvy -- An R package for modern methods for non-probability surveys

The following paper presents nonprobsvy -- an R package for inference based on non-probability samples. The package implements various approaches that can be categorized into three groups: prediction-based approach, inverse probability weighting and doubly robust approach. In the package, we assume the existence of either population-level data or probability-based population information and leverage the survey package for inference. The package implements both analytical and bootstrap variance estimation for the proposed estimators. In the paper we present the theory behind the package, its functionalities and case study that showcases the usage of the package. The package is aimed at scientists and researchers who would like to use non-probability samples (e.g.big data, opt-in web panels, social media) to accurately estimate population characteristics.

stat.ME↗

arXiv2024

singleRcapture: An R Package for Single-Source Capture-Recapture Models

Population size estimation is a major challenge in official statistics, social sciences, and natural sciences. The problem can be tackled by applying capture-recapture methods, which vary depending on the number of sources used, particularly on whether a single or multiple sources are involved. This paper focuses on the first group of methods and introduces a novel R package: singleRcapture. The package implements state-of-the-art single-source capture-recapture (SSCR) models (e.g.~zero-truncated one-inflated regression) together with new developments proposed by the authors, and provides a user-friendly application programming interface (API). This self-contained package can be used to produce point estimates and their variance and implements several bootstrap variance estimators or diagnostics to assess quality and conduct sensitivity analysis. It is intended for users interested in estimating the size of populations, particularly those that are difficult to reach or measure, for which information is available only from one source and dual/multiple system estimation is not applicable. Our package serves to bridge a significant gap, as the SSCR methods are either not available at all or are only partially implemented in existing R packages and other open-source software.

stat.AP↗

arXiv2024

Data integration of non-probability and probability samples with deterministic predictive mean matching

We study deterministic predictive mean matching mass imputation estimators to integrate data from probability and non-probability samples. We consider two approaches: predicted-to-predicted (PMM~A) and predicted-to-observed (PMM~B) matching. We prove the consistency of mean estimators, derive a variance decomposition, and propose estimators of variance. We establish consistency of the PMM~A estimator under model misspecification and underline key differences from the nearest neighbour method. Our PMM~B approach can be employed with non-parametric regression techniques, such as kernel regression, and the analytical expression for variance applies to nearest neighbour matching for non-probability samples. Extensive simulation studies compare properties of the proposed estimators with existing alternatives and examine the effects of model misspecification. The paper concludes with an empirical study on the integration of job vacancy survey and vacancies submitted to public employment offices (admin and online data). Open-source software is available.

stat.ME↗

arXiv2024

Quantile balancing inverse probability weighting for non-probability samples

The use of non-probability data sources for statistical purposes and for official statistics has become increasingly popular in recent years. However, statistical inference based on non-probability samples is made more difficult by nature of their biasedness and lack of representativity. In this paper we propose quantile balancing inverse probability weighting estimator (QBIPW) for non-probability samples. We apply the idea of Harms and Duchesne (2006) allowing the use of quantile information in the estimation process to reproduce known totals and the distribution of auxiliary variables. We discuss the estimation of the QBIPW probabilities and its variance. Our simulation study has demonstrated that the proposed estimators are robust against model mis-specification and, as a result, help to reduce bias and mean squared error. Finally, we applied the proposed methods to estimate the share of job vacancies aimed at Ukrainian workers in Poland using an integrated set of administrative and survey data about job vacancies.

stat.ME↗