Abstract
In this work, a method of Bayesian which is suggested for determine of outlier observation in the samples which has multivariate normal distribution is introduced. Outlier observation is introduced using distribution of quadratic forms in also sampling theory. Posterior odds of quadratic forms of errors are used to determine of observations. In aplication, posterior odds in the real data corresponding to every observation are found and outlier observations are determined.
References
- BARNETT, V. (1976), The Ordering Multivariate Data (Withdiscussion), J. Roy. Statist. Soc. Ser. A. 139, 318-54.
- BARNETT, V. LEWIS, T (1994), Outlier in Statistical Data, 3rd Ed. Chichester: John Wiley&Sons.
- BOX, G. E. P., TIAO, G. C. (1973), Bayesian Inference in Statistical Analysis, Reading, MA: Addison-Wesley.
- CAMPBELL, N (1980), Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation., Applied Statistics, 29, 231-37.
- CHALONER, K., BRANT, R. (1988), a Bayesian Approach to Outlier Detection and Residual Analysis., Biometrika, 75, 651-9.
- GNANADESIKAN, R., KETTENRING, J. (1972), Robust Estimates, Residuals and Outlier Detection with Multiresponse Data., Biometrics, 28, 81-124.
- GUTTMAN, I. (1973), Care and Handling of Univariate or Multivariate Outliers in Detecting Spuriosity-A Bayesian Approach., Technometrics. 15. 723-38.
- HAWKINS, D. (1980), Identification of Outliers, London, Chapman and Hall.
- JUSTEL, A., PENA, D. (2001), Bayesian Unmasking in Linear Models, Computational Statistics & Data Analysis. 36, 69-84.
- PETER M. LEE. (1989), Bayesian Statistics, London, Chapman and Hall.
- KASS, R., RAFTERY, A. (1995), Bayes Factors, JASA, 90, 773-95.
- KHATTREE R., NAIK N.D. (1999), Applied Multivariate Statistics with SAS Software, SAS Institute.
- ROUSSEEUW, P., LEROY, A. (1987), Robust Regression and Outlier Detection, New York: Wiley.
- ROUSSEEUW, P., VAN ZAMEREN, B. (1990), Unmasking Multivariate Outliers and Leverage Points, JASA, 85, 633-9.
Çok Değişkenli Normal Dağılıma Sahip Örneklerdeki Aykırı Gözlemlerin Belirlenmesi İçin Bayesgil Bir Yaklaşım
Abstract
Bu çalışmada, çok değişkenli normal dağılıma sahip örneklerdeki aykırı gözlemlerin belirlenmesi için önerilen bayesgil bir metod tanıtılmaktadır. Örnekleme teorisinde de kullanılan karesel formların dağılımından yararlanarak aykırı gözlemleri belirlemek fikrinden hareketle, gerçekleşmiş hataların karesel formlarının sonsal (posterior) dağılımı, bu gözlemlerin belirlenmesi için kullanılmaktadır. Uygulamada, gerçek bir veri üzerinde her bir gözleme ilişkin sonsal olasılıklar elde edilmiş ve aykırı (outliner) gözlem(ler) belirlenmiştir.
References
- BARNETT, V. (1976), The Ordering Multivariate Data (Withdiscussion), J. Roy. Statist. Soc. Ser. A. 139, 318-54.
- BARNETT, V. LEWIS, T (1994), Outlier in Statistical Data, 3rd Ed. Chichester: John Wiley&Sons.
- BOX, G. E. P., TIAO, G. C. (1973), Bayesian Inference in Statistical Analysis, Reading, MA: Addison-Wesley.
- CAMPBELL, N (1980), Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation., Applied Statistics, 29, 231-37.
- CHALONER, K., BRANT, R. (1988), a Bayesian Approach to Outlier Detection and Residual Analysis., Biometrika, 75, 651-9.
- GNANADESIKAN, R., KETTENRING, J. (1972), Robust Estimates, Residuals and Outlier Detection with Multiresponse Data., Biometrics, 28, 81-124.
- GUTTMAN, I. (1973), Care and Handling of Univariate or Multivariate Outliers in Detecting Spuriosity-A Bayesian Approach., Technometrics. 15. 723-38.
- HAWKINS, D. (1980), Identification of Outliers, London, Chapman and Hall.
- JUSTEL, A., PENA, D. (2001), Bayesian Unmasking in Linear Models, Computational Statistics & Data Analysis. 36, 69-84.
- PETER M. LEE. (1989), Bayesian Statistics, London, Chapman and Hall.
- KASS, R., RAFTERY, A. (1995), Bayes Factors, JASA, 90, 773-95.
- KHATTREE R., NAIK N.D. (1999), Applied Multivariate Statistics with SAS Software, SAS Institute.
- ROUSSEEUW, P., LEROY, A. (1987), Robust Regression and Outlier Detection, New York: Wiley.
- ROUSSEEUW, P., VAN ZAMEREN, B. (1990), Unmasking Multivariate Outliers and Leverage Points, JASA, 85, 633-9.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Statistics |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | April 15, 2003 |
| Published in Issue | Year 2003 Volume: 2 Issue: 1 |
