Research Article
BibTex RIS Cite

Lineer Modellerde Yarı Uzay Derinliğine Dayalı Dengeli Bootstrap Güven Bölgeleri

Year 2003, Volume: 2 Issue: 3, 63 - 72, 15.12.2003

Abstract

Bir lineer modelde parametrelere ilişkin güven bölgelerinin oluşturulmasında son yıllarda uygulaması yaygınlaşmaya başlayan derinlik kavramı kullanılarak dengeli bootstrap güven bölgelerinin nasıl oluşturulabileceği bir uygulama ile gösterilmiştir.

References

  • DONOHO. L. DAVID and GASKO, M. (1992). Estimates Based on Halfspace Depth and Projected Outlyingness. Ann. Statist., Vol. 20, No. 4, 1803-1827.
  • EFRON, B. ( 1982). The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia,PA, U.S.A
  • GRAYBILL, F. A. (1976). Theory and Application of the Linear Model. Duxbury Press, North Scituate , Mass., U.S.A.
  • HALL, P. (1992). The Bootstrap and Edgeworth Expansion. Springer-Verlag, New York. U.S.A..
  • LEHMANN, E. L. (1999). Elements of Large-Sample Theory. Springer-Verlag, New York, U.SA.
  • LIU, R. Y. (1990), on a Notion of Data Depth Based on Random Simplicies. Ann. Statis Vol. 18, No. 1,405-414.
  • LIU, REGINA Y., PARELIUS, JESSE M. and SINGH, K. (1999). Multivariate Analysis by Data Depth: Descriptive Statistics, Graphies and Inference. Ann. Statist., Vol. 27, No. 3, 783-858.
  • QUMSIYEH, MAHER B. (1994). Bootsrapping and Empirical Edgeworth Expansions in Multiple Lineer Regression Models. Commumications in Statistics: Theory and Methods, 23(11), 3227-3239.
  • ROUSSEEUW, PETER J. and RUTS, I. (1996). Bivariate Location Depth. Appl. Statis. Vol. 45, No:4, 516-526.
  • ROUSSEEUW, PETER J. and RUTS, I. (1999). The Depth Function of a Population Distribution. Metrika, 9, 213-244.
  • YEH, ARTHUR B. and SINGH, K. (1997). Balanced Confidence Regions Based on Tukey's Depth and the Bootstrap. J. R. Statist. Soc. B, Vol. 59, No.3, 639-652.
  • ZUO, Y. and SERFLING, R. (2000). Structural Properties and Convergence Results for Contours of Sample Statistical Depth Functions. Ann . Statist., Vol. 28, No. 2, 483-499.

Balanced Bootstrap Confidence Regions in Lineer Models Based on Half Space Depth

Year 2003, Volume: 2 Issue: 3, 63 - 72, 15.12.2003

Abstract

A balanced bootstrap confidence region has been studied and examplified for a linear model parameters by data depth a Notion which have become increasingly used in multivariate data analysis in recent years.

References

  • DONOHO. L. DAVID and GASKO, M. (1992). Estimates Based on Halfspace Depth and Projected Outlyingness. Ann. Statist., Vol. 20, No. 4, 1803-1827.
  • EFRON, B. ( 1982). The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia,PA, U.S.A
  • GRAYBILL, F. A. (1976). Theory and Application of the Linear Model. Duxbury Press, North Scituate , Mass., U.S.A.
  • HALL, P. (1992). The Bootstrap and Edgeworth Expansion. Springer-Verlag, New York. U.S.A..
  • LEHMANN, E. L. (1999). Elements of Large-Sample Theory. Springer-Verlag, New York, U.SA.
  • LIU, R. Y. (1990), on a Notion of Data Depth Based on Random Simplicies. Ann. Statis Vol. 18, No. 1,405-414.
  • LIU, REGINA Y., PARELIUS, JESSE M. and SINGH, K. (1999). Multivariate Analysis by Data Depth: Descriptive Statistics, Graphies and Inference. Ann. Statist., Vol. 27, No. 3, 783-858.
  • QUMSIYEH, MAHER B. (1994). Bootsrapping and Empirical Edgeworth Expansions in Multiple Lineer Regression Models. Commumications in Statistics: Theory and Methods, 23(11), 3227-3239.
  • ROUSSEEUW, PETER J. and RUTS, I. (1996). Bivariate Location Depth. Appl. Statis. Vol. 45, No:4, 516-526.
  • ROUSSEEUW, PETER J. and RUTS, I. (1999). The Depth Function of a Population Distribution. Metrika, 9, 213-244.
  • YEH, ARTHUR B. and SINGH, K. (1997). Balanced Confidence Regions Based on Tukey's Depth and the Bootstrap. J. R. Statist. Soc. B, Vol. 59, No.3, 639-652.
  • ZUO, Y. and SERFLING, R. (2000). Structural Properties and Convergence Results for Contours of Sample Statistical Depth Functions. Ann . Statist., Vol. 28, No. 2, 483-499.
There are 12 citations in total.

Details

Primary Language Turkish
Subjects Statistics
Journal Section Research Articles
Authors

İhsan Karabulut

Fikri Öztürk This is me

Publication Date December 15, 2003
Published in Issue Year 2003 Volume: 2 Issue: 3

Cite

APA Karabulut, İ., & Öztürk, F. (2003). Lineer Modellerde Yarı Uzay Derinliğine Dayalı Dengeli Bootstrap Güven Bölgeleri. İstatistik Araştırma Dergisi, 2(3), 63-72.