Testing inflated zeros and applications in right-censored geometric regression models

Liping Zhang, Gülistan Kurbanyaz, Jianxin Pan, Keming Yu, Wolfgang Karl Härdle and Maozai Tian ()
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Liping Zhang: Xinjiang University of Finance and Economics, School of Statistics and Data Science
Gülistan Kurbanyaz: Xinjiang University of Finance and Economics, School of Statistics and Data Science
Jianxin Pan: Beijing Normal - Hong Kong Baptist University, Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, Faculty of Science and Technology
Keming Yu: Brunel University London, Mathematical Sciences
Wolfgang Karl Härdle: Academy of Economic Sciences in Bucharest, Institute Digital Assets
Maozai Tian: Renmin University of China, Center for Applied Statistics, School of Statistics

Statistical Papers, 2025, vol. 66, issue 7, No 10, 39 pages

Abstract: Abstract Investigating the abundance of a particular species and its associated determinants often reveals that count data collected within sampling units contain a substantial proportion of zeros, while full sampling efforts are frequently limited by cost. The Zero-Inflated Right-Censored Geometric Regression (ZIRCGeR) model, which belongs to the family of right-censored count regression models, provides a flexible framework to address this challenge. Before applying the ZIRCGeR model, it is essential to examine the origin of the observed zeros. This involves distinguishing between structural zeros and those generated by the stochastic component of the count process to ensure appropriate model specification. To address this issue, we propose a novel statistical test that compares the observed number of zeros with the number expected under the Right-Censored Geometric Regression model. We derive an explicit expression for the test statistic based on the theory of estimating equations and establish its asymptotic properties. Extensive simulation studies were conducted to compare the performance of the proposed test with Wald, likelihood ratio, and Score tests. The results indicate that, in most scenarios, the proposed test exhibits clear advantages, particularly in controlling the Type I error rate. Finally, two empirical case studies involving bat population counts and plant abundance are conducted to demonstrate the practical utility and generalizability of the proposed test.

Keywords: Right-censored geometric regression model; Zero-inflated right-censored geometric regression model; Statistical tests; Type I error; Power (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01771-1

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