Showing papers by "Robert Tibshirani published in 1994"

Flexible Discriminant Analysis by Optimal Scoring

Abstract: Fisher's linear discriminant analysis is a valuable tool for multigroup classification. With a large number of predictors, one can find a reduced number of discriminant coordinate functions that are “optimal” for separating the groups. With two such functions, one can produce a classification map that partitions the reduced space into regions that are identified with group membership, and the decision boundaries are linear. This article is about richer nonlinear classification schemes. Linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups. In this paper, we obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method. In this way, any multiresponse regression technique (such as MARS or neural networks) can be postprocessed to improve its classification performance.

Adaptive Principal Surfaces

Abstract: We develop a nonlinear generalization of principal components analysis. A principal surface of the data is constructed adaptively, using some ideas from the MARS procedure of Friedman. We explore applications to curve and surface reconstruction and to data summarization.

Implications of Measurement Error in Exposure for the Sample Sizes of Case-Control Studies

Abstract: In this paper, recent results describing the effects of measurement error on estimation of the association between an exposure and a disease are applied to sample size calculation in case-control studies. Models of the relation between true exposure and a surrogate exposure measure assessed with error are used to derive equations for sample size determination. The results show that the sample size of a study based on an exposure variable which is measured with error must be larger by a factor of 1/rho 2 than if exposure were measured without error, where rho is the correlation between the true exposure and the surrogate exposure measure. Review of the magnitude of measurement error in dietary assessments suggests that failure to account for measurement error in sample size determination for case-control studies of diet and disease could lead to marked underestimation of the required sample size.

Some aspects of the reparametrization of statistical models

Abstract: Definitions are given for ortogonal parameters in the context of Bayesian inference and likelihood inference. The exact. orthogonalzing transfonnatioris are derived for. both cases , and the connection between the two settngs is made precise. These parametrzations simpliy the interpretation of likeliood functions and posterior distrbutions. Fuer, they make numerical maximzation and integration procedures easier to apply. Several applications are studied.