A Note on the Covariance Matrix of Order Statistics of Standard normal Observations

  • 발행 : 2000.04.01

초록

We noted a property of a stationary distribution on the matrix C, which is the covariance matrix of order statistics of standard normal distribution That is the sup norm of th powers of C is ee' divided by its dimension. The matrix C can be taken as a transition probability matrix in an acyclic Markov chain.

키워드

참고문헌

  1. Standard Probability and Statistics Tables and Formulae Beyer, W.H.
  2. Order Statistics David, H.A.
  3. The Theory of Matrices Gantmacher, F.R.
  4. Ann Math. Statist. v.37 Characterization of normal and generlized truncated normal distributions using order statistic Govindatajulu, Z.
  5. J. Statist. Plann. Infer. v.24 On the dependence structures of order statistics and concomitants of order statistics Kim, S.H.;David, H.A.
  6. Stat. Prob. Letters v.43 The joint covariance structure of ordered symmetrically dependent observations and their concomitants of order Lee, H.M.;Viana, M.
  7. J. Amer. Statist. Assn. v.90 Correlation analysis of extreme observations from a multivariate normal distribution Olkin, I.;Viana, M.
  8. Ann. Math. Statist. v.29 A problem of berkson, and minimum variance orderly estimation Tukey, J.
  9. On a class of patterned matrix Viana, M.
  10. Advances in Statistical Decision Theory and Application Correlation analysis of ordered observation from a block-equicorrelated multvariate normal distribution. Viana, M.;Olkin, I;S. Panchapakesan(ed.);N. Balakrihnan(ed.)