Given a polyhedron P by a list of inequalities we develop unbiased estimates of the number of vertices and bases of P . The estimates are based on applying tree estimation methods to the reverse search technique. The time to generate an unbiased estimate is essentially bounded by the time taken

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We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. k-means or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference

Abstract: Dramatic changes are occurring in the nature of international trade. Production processes increasingly involve a sequential, vertical trading chain stretching across many countries, with each country specializing in particular stages of a good’s production sequence. We document a key

In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors

for model-based clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, mineeld detection, cluster

The astonishing increase in computer performance over the past two decades has made it possible for economists to base many statistical inferences on simulated, or bootstrap, distributions rather than on distributions obtained from asymptotic theory. In this paper, I review some of the basic ideas of bootstrap inference. The paper discusses Monte Carlo tests, several types of bootstrap test, and bootstrap confidence intervals. Although bootstrapping often works well, it does not do so in every case.

Valid predictions for the direction of nonresponse bias were obtained from subjective estimates and extrapolations in an analysis of mail survey data from published studies. For estimates of the magnitude of bias, the use of extrapolations led to substantial improvements over a strategy

We describe and analyze a simple and effective stochastic sub-gradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ɛ is Õ(1/ɛ), where each iteration operates on a