中文摘要：

在大多数文献中,使用二项分布b（mi,pi）处理实际问题的时候通常都把mi当作常量来处理.这在有时候往往是比较片面的,因此在本文中考虑m_i为随机变量的情形,并且假设其服从截断泊松分布Truncated Poisson（λi）,称之为二项—泊松模型.我们主要基于惩罚极大似然的思想研究了二项-泊松模型的变量选择和参数估计问题.在一定的正则条件下,证明了所给出的变量选择具有相合性和Oracle性质.最后通过随机模拟研究了有限样本量下变量选择的表现,模拟研究显示变量选择效果较好.

英文摘要：

In most literature, we use the binomial distribution b（mi, pi） to deal with practi- cal problems and regard ms as a constant. However, it sometimes is one-sided. Therefore, in this paper we consider mi as a random variable, and assume that it follows truncated poisson distribution, then we call it binomial-poisson models. We propose a penalized maximum likelihood method for simultaneous variable selection in binomial-poisson models. Under certain regularity conditions, we establish the consistency and the oracle property of the variable selection. The proposed variable selection procedures perform well in simulation studies conducted in this paper.