Showing papers by "Robert Tibshirani published in 1991"

Statistical Data Analysis in the Computer Age

Abstract: Most of our familiar statistical methods, such as hypothesis testing, linear regression, analysis of variance, and maximum likelihood estimation, were designed to be implemented on mechanical calculators. Modern electronic computation has encouraged a host of new statistical methods that require fewer distributional assumptions than their predecessors and can be applied to more complicated statistical estimators. These methods allow the scientist to explore and describe data and draw valid statistical inferences without the usual concerns for mathematical tractability. This is possible because traditional methods of mathematical analysis are replaced by specially constructed computer algorithms. Mathematics has not disappeared from statistical theory. It is the main method for deciding which algorithms are correct and efficient tools for automating statistical inference.

The II P method for estimating multivariate functions from noisy data

Abstract: The Π method for estimating an underlying smooth function of M variables, (x l , …, xm ), using noisy data is based on approximating it by a sum of products of the form Π m φ m (x m ). The problem is then reduced to estimating the univariate functions in the products. A convergent algorithm is described. The method keeps tight control on the degrees of freedom used in the fit. Many examples are given. The quality of fit given by the Π method is excellent. Usually, only a few products are enough to fit even fairly complicated functions. The coding into products of univariate functions allows a relatively understandable interpretation of the multivariate fit.