Computation of the Frequency Function of a Quadratic Form in Random Normal Variables

Abstract

One of the outstanding problems in the theory of time series analysis is the distribution problem in spectral analysis for small samples. When the number of observations is sufficiently large for the Central Limit Theorem to be applicable, the normal approximation can be used to advantage. In recent years, work has aimed at the discovery of more generally applicable approximate methods and of more rational criteria for the sample size at which the large sample theory becomes useful; the state of the art is summarized in two recent papers by Grenander, Pollak and Slepian [1] and Freiberger and Grenander [2].