Zero-inflated models and estimation in zero-inflated Poisson distribution

In this paper, we briefly overview different zero-inflated probability distributions. We compare the performance of the estimates of Poisson, Generalized Poisson, ZIP, ZIGP and ZINB models through Mean square error (MSE), bias and Standard error (SE) when the samples are generated from ZIP distribution. We propose a new estimator referred to as probability estimator (PE) of inflation parameter of ZIP distribution based on moment estimator (ME) of the mean parameter and compare its performance with ME and maximum likelihood estimator (MLE) through a simulation study. We use the PE along with ME and MLE to fit ZIP distribution to various zero-inflated datasets and observe that the results do not differ significantly. We recommend using PE in place of MLE since it is easy to calculate and the simulation study in this paper demonstrates that the PE performs as good as MLE irrespective of the sample size.     

Zero-inflated and overdispersed: what's one to do?

Zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models are recommended for handling excessive zeros in count data. For various reasons, researchers may not address zero inflation. This paper helps educate researchers on (1) the importance of accounting for zero inflation and (2) the consequences of misspecifying the statistical model. Using simulations, we found that when the zero inflation in the data was ignored, estimation was poor and statistically significant findings were missed. When overdispersion within the zero-inflated data was ignored, poor estimation and inflated Type I errors resulted. Recommendations on when to use the ZINB and ZIP models are provided. In an illustration using a two-step model selection procedure (likelihood ratio test and the Vuong test), the ZIP model was correctly identified only when the distributions had moderate means and sample sizes and did not correctly identify the ZINB model or the zero inflation in the ZIP and ZINB distributions.     

关于股权众筹的影响因子分析——以“大家投”平台为例

作为新兴的互联网融资工具，众筹融资模式发展迅速。在金融市场最发达的美国，其学术界已开启了关于众筹平台上投资者决策的影响因素的探索性假说论证和实证检验，为未来众筹平台的发展提供了宝贵的前沿理论基础。然而不同众筹模式下平台的机制存在差异，并且不同文化地缘的投资者行为决策并不具有同质性，对于当前焦点的股权众筹业是否能够采纳这些观点仍然没有定论。本文以“大家投”平台数据为样本，采用零膨胀负二项回归对中国众筹平台项目筹资影响因素进行实证检验，期望给未来研究提供帮助。     

健康与贸易,孰轻孰重?——SPS措施的保护目的探讨

卫生与植物检疫（SPS）措施是各国以科学为依据制定的保护消费者健康和环境安全的法规标准。随着SPS措施在国际贸易中的广泛使用，其保护目标常常被质疑是为了保护贸易，而非健康。本文基于2001—2018年WTO成员针对农产品的SPS通报数据，分别选取代表“健康保护”和“贸易保护”的指标，采用零膨胀负二项回归模型（ZINB），研究SPS措施的保护目的。结果发现，与健康相关的变量与WTO成员的SPS措施通报数显著相关，SPS措施主要是为了保护消费者的健康，但也存在贸易保护的嫌疑；发达国家SPS措施保护贸易的嫌疑更大；加工农产品SPS措施相比初级农产品更具有贸易保护倾向。     

Dynamic changepoint detection in count time series: a particle filter approach

We study Bayesian dynamic models for detecting changepoints in count time series that present structural breaks. As the inferential approach, we develop a parameter learning version of the algorithm proposed by Chopin [Chopin N. Dynamic detection of changepoints in long time series. Annals of the Institute of Statistical Mathematics 2007;59:349–366.], called the Chopin filter with parameter learning, which allows us to estimate the static parameters in the model. In this extension, the static parameters are addressed by using the kernel smoothing approximations proposed by Liu and West [Liu J, West M. Combined parameters and state estimation in simulation-based filtering. In: Doucet A, de Freitas N, Gordon N, editors. Sequential Monte Carlo methods in practice. New York: Springer-Verlag; 2001]. The proposed methodology is then applied to both simulated and real data sets and the time series models include distributions that allow for overdispersion and/or zero inflation. Since our procedure is general, robust and naturally adaptive because the particle filter approach does not require restrictive specifications to ensure its validity and effectiveness, we believe it is a valuable alternative for dealing with the problem of detecting changepoints in count time series. The proposed methodology is also suitable for count time series with no changepoints and for independent count data.