**5.2 Some related recent literature**

Other researchers have considered the problem of the choice of the number of principal components. For example, Bai et al. [11] examined the asymptotic consistency of AIC and BIC for determining the number of significant principal components in high-dimensional problems. The focus in this chapter has not necessarily been on high-dimensional problems.

Some various applications from recent literature involving choosing the number of principal components include the following. The method presented here could possibly be applied in these applications.

For example, a good book on the topic of model selection and testing, covering many aspects, is [12]. In recent years, various econometricians have examined the problems of diagnostic testing, specification testing, semiparametric estimation, and model selection. In addition, various researchers have considered whether to use model testing and model selection procedures to decide upon the models that best fit a particular dataset. This book explores both the issues with application to various regression models, including models for arbitrage pricing theory. Along the lines of model selection criteria, the book references, e.g., [8], the foundational paper for BIC.

Next, we mention some recent papers, which show applications of model selection in various research areas.

One such paper is [13], an application of principal component analysis and other methods to water quality assessment in a lake basin in China.

Another is [14], on feature selection for *classification* using principal component analysis.

As mentioned, a particularly interesting application of principal component analysis is in regression and logistic regression. We have mentioned the paper [10] on using principal component analysis in regression, taking several principal components to replace the set of explanatory variables. Another interesting application is in [15], on using principal components in *logistic* regression.
