We consider inference for functions of the marginal covariance matrix under a class of stationary vector time series models, referred to as time-orthogonal principal components models. The main application which motivated this work involves the estimation of configurational entropy from molecular dynamics simulations in computational chemistry, where current methods of entropy estimation involve calculations based on the sample covariance matrix. The theoretical results we obtain provide a basis for approximate inference procedures, including confidence interval calculations for scalar quantities of interest; these results are applied to the molecular dynamics application, and some further applications are discussed briefly.
Autoregressive Central limit theorem Configurational entropy Principal components Procrustes Sample covariance Shape Size-and-shape
This is a preview of subscription content, log in to check access.
Goodman N.R. (1963) Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction). Annals of Mathematical Statistics 34: 152–177zbMATHCrossRefMathSciNetGoogle Scholar
Harris S.A., Gavathiotis E., Searle M.S., Orozco M., Laughton C.A. (2001) Co-operativity in drug-DNA recognition: a molecular dynamics study. Journal of the American Chemical Society 123: 12658–12663CrossRefGoogle Scholar