Abstract
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.
Similar content being viewed by others
References
Arcones M.A. (1994) Limit theorems for nonlinear functionals of a stationary Gaussian field of vectors. Annals of Probability 22: 2242–2274
Cox D.R., Miller H.D. (1965) The theory of stochastic processes. Chapman and Hall, London
Dryden I.L., Mardia K.V. (1998) Statistical shape analysis. Wiley, Chichester
Goodman N.R. (1963) Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction). Annals of Mathematical Statistics 34: 152–177
Hannan E.J. (1976) The asymptotic distribution of series covariances. Annal of Statistics 4: 396–399
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: 12658–12663
Mardia K.V., Kent J.T., Bibby J.M. (1979) Multivariate analysis. Academic Press, London
Schlitter J. (1993) Estimation of absolute entropies of macromolecules using the covariance matrix. Chemical Physics Letters 215: 617–621
Siddiqui M.M. (1958) On the inversion of the sample covariance matrix in a stationary autoregressive process. Annals of Mathematical Statistics 29: 585–588
Watson G.S. (1983) Statistics on Spheres. University of Arkansas lecture notes in the mathematical sciences (Vol 6). Wiley, New York
Whittle P. (1953) Estimation and information in stationary time series. Arkiv För Matematik 2: 423–434
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Dryden, I.L., Kume, A., Le, H. et al. Statistical inference for functions of the covariance matrix in the stationary Gaussian time-orthogonal principal components model. Ann Inst Stat Math 62, 967–994 (2010). https://doi.org/10.1007/s10463-008-0202-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10463-008-0202-4