指数族非线性模型的统计诊断及其试验设计

【作者】 谢五三；

【导师】 冯予；

【作者基本信息】 南京理工大学 ， 应用数学， 2005， 硕士

【摘要】 本文首先对均值漂移模型建立几何结构，给出了该模型的两类曲率立体阵，由此推出了参数的最大似然估计量的二阶展开式，进而得到了基于曲率的诊断统计量，然后推得带线性约束指数族非线性模型的基于统计曲率的二阶诊断统计量。再计算模型的回归参数β在1-α置信水平下的置信域的体积，为了便于计算，需把置信域投影到切空间中去，投影后的置信域是一个椭球体，用Taylor展开方法对此椭球体的体积进行二阶近似，推出原参数置信域的体积的近似表达式，然后对回归模型进行试验设计，根据使置信域体积最小准则，在模型函数的设计变量的定义域上确定点列，选取使置信域体积达到最小的设计点。更多还原

【Abstract】 This paper first builds the geometric framework for the mean shift model, then gives two kinds of the curvature arrays and gets the second order expression of the MLE of the parameter, and then carries out the expression of the diagnostic statistic with the curvature array, and also carries out the second-order diagnostic statistic for the models with linear restriction. Second we calculate the volume of the confidence region of the parameters βwith a confidence level 1 - α , in order to make the calculating easier, it is necessary to map the confidence region into tangent space, and the confidence region, which, after having been mapped, will present itself as an ellipsoid. We use the Taylor series expansion method to get the second-order approximate expression of the confidence region of the parameters, and then according to the principle of minimizing the volume of the confidence region, this paper carries out experimental design for the regression model, and then fixes the point range in the domain of definition of design variable for the model function so as to select the designing point, which can minimize the volume of the confidence region.更多还原