We investigate the issue of post-selection inference for a fixed and a mixed parameter in a linear mixed model using a conditional Akaike information criterion as a model selection procedure. Within the framework of linear mixed models we develop complete theory to construct confidence intervals for regression and mixed parameters under three frameworks: nested and general model sets as well as misspecified models. Our theoretical analysis is accompanied by a simulation experiment and a post-selection examination on mean income across Galicia's counties. Our numerical studies confirm a good performance of our new procedure. Moreover, they reveal a startling robustness to the model misspecification of a naive method to construct the confidence intervals for a mixed parameter which is in contrast to our findings for the fixed parameters.

翻译：我们用一个有条件的Akaike信息标准作为模式选择程序,调查线性混合模型中固定和混合参数的选后推论问题。在线性混合模型框架内,我们开发了完整的理论,以构建三个框架下的回归和混合参数的信心间隔:嵌套式和通用模型以及错误描述模型。我们的理论分析伴随着对加利西亚各县平均收入的模拟实验和选后检查。我们的数字研究证实了我们新程序的良好表现。此外,这些研究显示,模型对构建混合参数信任间隔的天真的方法的错误描述令人惊异,这与我们对固定参数的调查结果形成对照。