In a system of N sensors, the sensor (formula available in paper) The problem is to estimate a fusion rule (formula available in paper), based on the sample, such that the expected square error is minimized over a family of functions F that constitute a vector space. The function f* that minimizes the expected error cannot be computed since the underlying densities are unknown, and only an approximation f to f* is feasible. We estimate the sample size sufficient to ensure that f provides a close approximation to f* with a high probability. The advantages of vector space methods are two-fold: (1) the sample size estimate is a simple function of the dimensionality of F, and (2) the estimate f can be easily computed by well-known least square methods in polynomial time. The results are applicable to the classical potential function methods and also (to a recently proposed) special class of sigmoidal feedforward neural networks.