Journal of the Korean Statistical Society

  • 제22권2호
  • /
  • Pages.249-258
  • /
  • 1993
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

An Efficient Computing Method of the Orthogonal Projection Matrix for the Balanced Factorial Design

  • 발행 : 1993.12.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

키워드

참고문헌

  1. Statistical computing Kenedy,W.J.;Gentle,J.E.
  2. Journal of the Korean Statistical Society v.15 The Moore-Penrose inverse for the classification models Kim,B.C.;Lee,J.T.
  3. Journal of the Japanese Society of Computational Statistics v.5 The orthogonal projection matrix for the unbalanced factorial design Kim,B.C.;Park,J.T.
  4. Journal of the Japanese Society of Computational Statistics v.2 The Moore-Penrose inverse for the balanced ANOVA models Kim,B.C.;Sunwoo,H.S.
  5. Journal of the Japanese Society of Computational Statistics v.3 The M-P inverse for the balanced factorial design with interactions Kim,B.C.;Sunwoo,H.S.
  6. The American Statistician v.36 An introduction to modern matrix methods and statistics Lowerre,J.M.
  7. Sankhya, Indian Journal of Statistics v.36 Rank conditions for generalized inverses of partitioned matrices Marsaglia,G.;Styan,G.P.H.
  8. The American Statistician v.38 Kronecker products in ANOVA - A first step Rogers,G.S.
  9. Matrix algebra useful for statistics Searle,S.R.