Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Variable Selection Theorem for the Analysis of Covariance Model

공분산분석 모형에서의 변수선택 정리

  • Yoon, Sang-Hoo (Department of Statistics, Chonnam National University) ;
  • Park, Jeong-Soo (Department of Statistics, Chonnam National University)
  • Published : 2008.05.30
Download PDF
⟨ Previous Next ⟩

Abstract

Variable selection theorem in the linear regression model is extended to the analysis of covariance model. When some of regression variables are omitted from the model, it reduces the variance of the estimators but introduces bias. Thus an appropriate balance between a biased model and one with large variances is recommended.

회귀모형에서의 변수선택에 관한 정리를 공분산분석 모형으로 확장하였다. 공분산분석 모형에서 몇개의 회귀변수를 제거한 축소모형을 세우는 경우에 추정량의 변화를 알아본 결과, 회귀계수 뿐만아니라 분산분석계수도 추정량의 편차는 증가하지만 분산은 감소하며, 어떤 경우에는 평균제곱오차도 감소한다는 결론을 얻었다.

Keywords

References

  1. 김진흠, 김민호 (2004). 변수선택 편향이 없는 회귀나무를 만들기 위한 알고리즘, <응용통계연구>, 17,459-473
  2. 박성현 (1980). <회귀분석>, 민영사, 서울
  3. 박종선 (2007). Variable selection in sliced inverse regression using generalized eigenvalue problem with penalties, <한국통계학회논문집>, 14,215-227 https://doi.org/10.5351/CKSS.2007.14.1.215
  4. 윤영주,송문섭 (2005).Variable selection via penalized regression, <한국통계학회논문집>,12, 615-624 https://doi.org/10.5351/CKSS.2005.12.3.615
  5. 홍종선, 함주형, 김호일 (2005). 수정 결정계수를 사용한 로지스틱 회귀모형에서의 변수 선택법, <응용통계연구>, 18,435-443 https://doi.org/10.5351/KJAS.2005.18.2.435
  6. Choi, S. H. (2006). Interval regression models using variable selection, <한국통계학회논문집>,13, 125-134 https://doi.org/10.5351/CKSS.2006.13.1.125
  7. Claeskens, G., Croux, C. and Van Kerckhoven, J. (2006). Variable selection for logistic regression using a prediction-focused information criterion, Biometrics, 62, 972- 979 https://doi.org/10.1111/j.1541-0420.2006.00567.x
  8. George, E. I. (2000). The variable selection problem, Journal of the American Statistical Association, 95, 1304-1308 https://doi.org/10.2307/2669776
  9. Gurka, M. J. (2006). Selecting the best linear mixed model under REML, The American Statistician, 60, 19-26 https://doi.org/10.1198/000313006X90396
  10. Hocking, R. R. (1976). The Biometrics invited paper. The analysis and selection of variables in linear regression, Biometrics, 32, 1-49 https://doi.org/10.2307/2529336
  11. Kadane, J. B. and Lazar, N. A. (2004). Methods and criteria for model selection, Journal of the American Statistical Association, 99, 279-290 https://doi.org/10.1198/016214504000000269
  12. Ravishanker, N. and Dey, D. K. (2001). A First Course in Linear Model Theory, Chap- man & Hall/CRC, New York
  13. Rencher, A. C. (2000). Linear Models in Statistics, John Wiley & Sons, New York
  14. Seber, G. A. F. and Lee, A. J. (2003). Linear Regression Analysis, 2nd edition. John Wiley & Sons, New York
  15. Yuan, M. and Lin, Y. (2005). Efficient empirical Bayes variable selection and estimation in linear models, Journal of the American Statistical Association, 100, 1215-1225 https://doi.org/10.1198/016214505000000367