Lineer Modellerde Yarı Uzay Derinliğine Dayalı Dengeli Bootstrap Güven Bölgeleri
Year 2003,
Volume: 2 Issue: 3, 63 - 72, 15.12.2003
İhsan Karabulut
,
Fikri Öztürk
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
İhsan Karabulut
,
Fikri Öztürk
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.