Variance Reduction with Monte Carlo Estimates of Error rates in multivariate classification C.Weihs" G.Calzolari Fachbereich Statistik Dipartimento di Statistica Universitat Dortmund Universita degli studi di Firenze M.C.Rohl Konigstein /Ts August 1999 Abstract In this paper,control variates are proposed to speed up Monte Carlo Sim- ulations to estimate expected error rates in multivariate classification. KEY WORDS:classification,control variates,error rate,Monte Carl Simulation,variance reduction 1 Introduction The aim of this paper is to speed up Monte Carlo Simulations applied to multivariate classification.The most interesting performance measure in classification is the misclassification error. In the case of given group densities,there are two possibilities to calculate the error rate:either by numerical integration or by Monte Carlo Simulation which is the only feasible method in higher dimensions.In this paper,we focus on the Monte Carlo error estimate.This approach suffers from the variability of the error rates,because the error rate is a random variable by now.Therefore,every principle to reduce this variance is welcome.In the literature various variance reduction techniques are proposed,among those antithetic variables and control variates(see,e.g.,[1]).Here, *D-44221 Dortmund,Germany,Tel.++49231-755-4363,e-m ail:weihs@amadeus.st atistik.uni- dortmund.deVariance Reduction with Monte Carlo Estimates of Error Rates in Multivariate Classication C. Weihs Fachbereich Statistik Universitat Dortmund G. Calzolari Dipartimento di Statistica Universita degli studi di Firenze M. C. Rohl Konigstein /Ts. August 1999 Abstract In this paper, control variates are proposed to speed up Monte Carlo Sim￾ulations to estimate expected error rates in multivariate classication. KEY WORDS: classication, control variates, error rate, Monte Carlo Simulation, variance reduction 1 Introduction The aim of this paper is to speed up Monte Carlo Simulations applied to multivariate classication. The most interesting performance measure in classication is the misclassication error. In the case of given group densities, there are two possibilities to calculate the error rate: either by numerical integration or by Monte Carlo Simulation which is the only feasible method in higher dimensions. In this paper, we focus on the Monte Carlo error estimate. This approach suers from the variability of the error rates, because the error rate is a random variable by now. Therefore, every principle to reduce this variance is welcome. In the literature various variance reduction techniques are proposed, among those antithetic variables and control variates (see, e.g., [1]). Here, D-44221 Dortmund, Germany, Tel. ++49-231-755-4363, e-mail: weihs@amadeus.statistik.uni￾dortmund.de