A new nonparametric procedure designed for simulation studies

Abstract

This paper demonstrates how certain statistics, computed from a sample of size n (from almost any distribution) may be simulated by using a sequence of substantially less than n random normal variates. Many statistics, θ, including almost all maximum likelihood estimates, can be expressed in terms of the sample trigonometric moments, STM. The STM are asymptotically multivariate normal with a mean vector and variance-covariance matrix easily expressible in terms of equally spaced characteristic function evaluations. Thus one only needs to know the Fourier transform or equivalently the characteristic function associated with elements of any moderate to large i. i. d. sample and have access to a normal random number generator to generate a sequence of STM with distributional properties almost identical to those of STM computed from that sample. These STM can in turn be used to compute the desired statistic θ.

Keywords:

• Fourier series
• sample size
• data analysis
• asymptotic normality
• series term variance-covariance
• model-free
• histogram