On the Application of AIC to Bivariate Density Estimation, Nonparametric Regression and Discrimination
Some simple data analytic procedures are available for bivariate nonparametric density estimation. If we use a linear approximation of specified basis functions then the coefficients can be estimated by the EM algorithm, and the number of terms judged by Akaike’s information criterion. The method also yields readily compatible approaches to nonparametric regression and logistic discrimination. Tukey’s energy consumption data and a psychological test for 25 normal and 25 psychotic patients are re-analyzed and the current methodology compared with previous procedures. The procedures offer many possible applications in the biomedical area, which are discussed in Sections 5 and 6, e.g. it is possible to analyze noisy data sets in situations where structured regression techniques would typically fail.
KeywordsAIC Roughness parameter Bias Variance Tradeoff
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