Pseudo Maximum Likelihood Methods: Applications to Poisson Models
伪极大似然方法：泊松模型的应用AI 解读 ↓
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伪极大似然方法：泊松模型的应用
- 研究问题
- 当泊松计数模型存在分布设定误差时，能否不指定扰动的概率密度仍获得一致且渐近正态的估计，并比较不同方法的效率？
- 方法与思路
- 作者将伪极大似然用于基本及存在设定误差的泊松模型，比较有限样本与渐近性质，并提出准广义伪极大似然估计量。
- 材料陈述的贡献
- 摘要称可在不指定扰动密度时得到一致且渐近正态的估计，并提出在所研究伪极大似然估计类中渐近占优的准广义方法。
- 阅读关注点
- 核对允许的设定误差、一致性和渐近正态性的条件，以及渐近占优所用的比较标准；另查看双变量与面板模型的具体处理。
- 阅读边界
- 摘要未列出关键正则条件、有限样本比较结果和面板结构；不能将其结论理解为泊松模型在任意错误设定下都保持一致性。
原文摘要
Pseudo maximum likelihood techniques are applied to basic Poisson models and to Poisson models with specification errors. In the latter case it is shown that consistent and asymptotically normal estimators can be obtained without specifying the p.d.f. of the disturbances. These estimators are compared both from the finite sample and the asymptotic point of view. Quasi generalized PML estimators, which asymptotically dominate all PML estimators, are also proposed. Finally, bivariate and panel data Poisson models are discussed. THE ANALYSIS OF ECONOMIC BEHAVIOR often leads to the study of characteristics taking a small number of positive values. The classical linear model is not adapted to explain how such discrete variables depend on other quantitative or qualitative variables. The reasons are similar to those usually given in the case of an endogenous qualitative variable: the shape of the observation set does not correspond to a linear model, the assumption of normality of the disturbances cannot be made, since the endogenous variables take a small number of values with strictly positive probabilities, and the prediction formulae which are deduced from a linear model give impossible values. In the models considered in the literature to describe discrete variables (Cox and Lewis [2], El. Sayyad [3], Frome, Kutner, and Beauchamp [4], Gilbert [5], Hausman, Hall, and Griliches [8]; see also Lancaster [12]) the endogenous variable is assumed to have a Poisson distribution conditional upon the exogenous variables. The parameter of this distribution is a function of the values of the exogenous variables. The choice of such a model is justified if the dependent variable counts the occurrence of a given event during a fixed period and if the usual assumptions of the Poisson process are satisfied. For instance, the model is adapted to describe daily numbers of oil tankers' arrivals in a port, the number of accidents at work by factory, or the number of patents applied for and received by firms (Hausman, Hall, and Griliches [8]).