非线性再生散度模型的广义变离差检验

研究了非线性再生散度模型的广义变离差检验,对于一类常见的正则散度分布族,解决了离差参数的齐性检验问题,得到了检验的似然比统计量和score统计量,并证明了score统计量的渐近χ2性.本文研究的非线性再生散度模型包括了许多常见的统计模型,诸如正态线性和非线性回归模型、广义线性模型和广义非线性模型等;同时,本文结果也适用于某些更复杂的分布,诸如基于极值分布、单纯形分布的非线性模型等.因此本文的结果进一步推广和发展了文献中已有的工作.

Testing for Generalized Varying Dispersion in Nonlinear Reproductive Dispersion Models

In this paper,the testing for generalized varying dispersion is investigated in nonlinear reproductive dispersion models. For a common class of reproductive dispersion families, we obtain the likelihood ratio statistic and score statistic for the test. The asymptotic Xz proporty of score statistic is also proved. The model studied in this paper is much wider,so that many well-known nonlinear models are special cases of ours, such as normal linear and nonlinear models, generalized linear and nonlinear models, and the nonlinear models based on the extreme distribution or simplex distribution etc. Therefore,the results of this paper can be applied to these models.