Linear models as working models have performed very well in practice. But most often the theoretical properties are obtained under the usual linear model assumptions such as linearity, homoscedasticity and normality. Using the least squared estimators we justify their desirable properties under much broader model assumptions, namely a model lean framework. Generalized CP (GCP) is proposed to estimate the prediction errors. We study its properties. An alternative bootstrap method is also investigated. Model selections are done through both methods.
Joint work with Junhui Cai, Linda Zhao and the Wharton group