Spectral Analysis for Discrete Longitudinal Data

Abstract We develop a Fourier type of analysis for data consisting of many short strings X 1 , X 2 , ..., X n , with X i = ( X i 1 , ..., X ip ). The paper offers an approach testing and residual analysis based on a group theoretic decomposition of the sample space. This is illustrated on a physical chance type data set where it is natural to allow each string to have its own parameter (i.i.d. coin-tossing with parameter varying from string to string). The usual model is rejected.