Bandwidth choice for nonparametric classification

It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same signs, then minimum Bayes risk is achieved using bandwidths which are an order of magnitude larger than those which minimize pointwise estimation error. On the other hand, if the curvature signs are different, or if there are multiple crossing points, then bandwidths of conventional size are generally appropriate. The range of different modes of behavior is narrower in multivariate settings. There, the optimal size of bandwidth is generally the same as that which is appropriate for pointwise density estimation. These properties motivate empirical rules for bandwidth choice

Bandwidth choice for nonparametric classification

It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same signs, then minimum Bayes risk is achieved using bandwidths which are an order of magnitude larger than those which minimize pointwise estimation error. On the other hand, if the curvature signs are different, or if there are multiple crossing points, then bandwidths of conventional size are generally appropriate. The range of different modes of behavior is narrower in multivariate settings. There, the optimal size of bandwidth is generally the same as that which is appropriate for pointwise density estimation. These properties motivate empirical rules for bandwidth choice.Comment: Published at http://dx.doi.org/10.1214/009053604000000959 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Modeling College Major Choices Using Elicited Measures of Expectations and Counterfactuals

The choice of a college major plays a critical role in determining the future earnings of college graduates. Students make their college major decisions in part due to the future earnings streams associated with the different majors. We survey students about what their expected earnings would be both in the major they have chosen and in counterfactual majors. We also elicit students' subjective assessments of their abilities in chosen and counterfactual majors. We estimate a model of college major choice that incorporates these subjective expectations and assessments. We show that both expected earnings and students' abilities in the different majors are important determinants of student's choice of a college major. We also show that students' forecast errors with respect to expected earnings in different majors is potentially important, with our estimates suggesting that 7.5% of students would switch majors if they made no forecast errors.choice of college major, subjective expectations