Efficiency of multivariate control variates in Monte Carlo simulation. (English) Zbl 0606.65100

Rubinstein, Reuven Y.; Marcus, Ruth

Oper. Res. 33, 661-677 (1985).

This paper considers some statistical aspects of applying control variates to achieve variance reduction in the estimation of a vector of response variables in Monte Carlo simulation. It gives a result that quantifies the loss in variance reduction caused by the estimation of the optimal control matrix. For the one-dimensional case, we derive analytically the optimal size of the vector of control variates under specific assumptions on the covariance matrix. For the multidimensional case, our numerical results show that good variance reduction is achieved when the number of control variates is relatively small (approximately of the same order as the number of unknown parameters). Finally, we give some recommendations for future research.

MSC:

65C99	Probabilistic methods, stochastic differential equations
65C05	Monte Carlo methods
62J10	Analysis of variance and covariance (ANOVA)
62F99	Parametric inference

Keywords:

multivariate control variates; variance reduction; Monte Carlo simulation; optimal control matrix