Uses of the fast Fourier transform (FFT) in exact statistical inference

We present a unified characteristic function-based framework to compute exact statistical inference. The methodology is implemented using the fast Fourier transform (FFT) algorithm. Exact p-values for hypotheses of interest are obtained for generalized linear models (GLMs) commonly used in medical and other applied sciences. Examples are shown to illustrate the ease with which the FFT is used to recover exact probabilities from any known characteristic function.;The framework we developed allowed us to incorporate models based on non-standard underlying error distributions such as the zero-truncated binomial and Poisson distributions. We also have used the methodology to investigate the sensitivity of exact significance levels to misclassification errors and other model mis-specifications. Potential sources of errors in using the FFT are discussed.