Sensitivity analysis in linear models

Shuangzhe Liu; Tiefeng Ma; Yonghui Liu

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 225-232
  • ISSN: 2300-7451

Abstract

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In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators’ sensitivity results.We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.

How to cite

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Shuangzhe Liu, Tiefeng Ma, and Yonghui Liu. "Sensitivity analysis in linear models." Special Matrices 4.1 (2016): 225-232. <http://eudml.org/doc/277081>.

@article{ShuangzheLiu2016,
abstract = {In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators’ sensitivity results.We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.},
author = {Shuangzhe Liu, Tiefeng Ma, Yonghui Liu},
journal = {Special Matrices},
keywords = {elliptical distribution; least squares; maximum likelihood; mixed estimation; sensitivity matrix},
language = {eng},
number = {1},
pages = {225-232},
title = {Sensitivity analysis in linear models},
url = {http://eudml.org/doc/277081},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Shuangzhe Liu
AU - Tiefeng Ma
AU - Yonghui Liu
TI - Sensitivity analysis in linear models
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 225
EP - 232
AB - In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators’ sensitivity results.We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.
LA - eng
KW - elliptical distribution; least squares; maximum likelihood; mixed estimation; sensitivity matrix
UR - http://eudml.org/doc/277081
ER -

References

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  1. [1] A. N. Banerjee, J. R. Magnus, The sensitivity of OLS when the variance matrix is (partially) unknown, J. Econometrics 92, 295–323 (1999) [Crossref] Zbl0951.62050
  2. [2] R. D. Cook, Influential observations in linear regression, J. Amer. Statist. Assoc. 74, 169–74 (1979) [Crossref] Zbl0398.62057
  3. [3] R. D. Cook, Assessment of local influence (with discussion), J. Royal Statist. Soc. Ser. B 48, 133-169 (1986)  Zbl0608.62041
  4. [4] K. T. Fang, S. Kotz, S., K. W. Ng, Symmetric Multivariate and Related Distributions (Chapman, London, 1990)  Zbl0699.62048
  5. [5] K. T. Fang, Y. T. Zhang, Generalized Multivariate Analysis (Springer, Berlin, 1990)  Zbl0724.62054
  6. [6] M. H. J. Gruber, Regression Estimators: A Comparative Study (John Hopkins University Press, Baltimore, MD, 2010)  Zbl1216.62100
  7. [7] C. Hao, D. von Rosen, T. von Rosen, Explicit influence analysis in two-treatment balanced crossover models,Math. Methods Statist., 24, 16-36 (2015) [Crossref] Zbl1328.62418
  8. [8] T. Kollo, D. von Rosen, Advanced Multivariate Statistics with Matrices (Springer, Dordrecht, 2005)  Zbl1079.62059
  9. [9] V. Leiva, S. Liu, L. Shi, F. J. A. Cysneiros, Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics, J. Appl. Statist. (2016) [Crossref] 
  10. [10] S. Liu, Contributions to Matrix Calculus and Applications in Econometrics (Thesis Publishers, Amsterdam, 1995)  
  11. [11] S. Liu, S. E. Ahmed, L. Y.Ma, Influence diagnostics in the linear regression modelwith linear stochastic restrictions, Pakistan J. Statist. 25, 647-662 (2009)  
  12. [12] S. Liu, T. Ma, W. Polasek, Spatial system estimators for panel models: a sensitivity and simulation study, Math. Comput. Simul. 101, 78-102 (2014) [Crossref][WoS] 
  13. [13] S. Liu, H. Neudecker, Local sensitivity of the restricted least squares estimator in the linear model, Statist. Pap. 48, 525 (2007)  
  14. [14] S. Liu, W. Polasek, R. Sneller, Sensitivity analysis of SAR estimators: a numerical approximation, J. Statist. Comput. Simul. 82(2), 325-342 (2012) [Crossref] Zbl06154792
  15. [15] Y. Liu, G. Ji, S. Liu, Influence diagnostics in a vector autoregressive model, J. Statist. Comput. Simul. 85(13), 2632-2655 (2015) [Crossref] 
  16. [16] J. R.Magnus, H. Neudecker,Matrix Differential Calculus with Applications in Statistics and Econometrics (Wiley, Chichester, 1999)  Zbl0912.15003
  17. [17] J. R. Magnus, A. L. Vasnev, Local sensitivity and diagnostic tests, Econometrics J. 10(1), 166-192 (2007)  Zbl1116.62078
  18. [18] J. X. Pan, , K. T. Fang, D. von Rosen, Local influence assessment in the growth curve model with unstructured covariance, J. Statist. Plann. Inference 62, 263-278 (1997) [Crossref] Zbl0917.62053
  19. [19] W. Polasek, Regression diagnostics for general linear regression models, J. Amer. Statist. Assoc. 79, 336-340 (1984) [Crossref] Zbl0581.62054
  20. [20] W. Polasek, Local sensitivity analysis and Bayesian regression diagnostics, In P. K. Goel, A. Zellner, (Ed.), Bayesian Inference and Decision Techniques (North-Holland, Amsterdam, (1986) 375-387  
  21. [21] S. Puntanen, G. P. H. Styan, J. Isotalo,Matrix Tricks for Linear Statistical Models – Our Personal Top Twenty (Springer, Berlin, 2011)  Zbl1291.62014
  22. [22] C. R. Rao, H. Toutenburg, Shalabh, C. Heumann, Linear Models and Generalizations (Springer, Berlin, 2008)  Zbl1151.62063
  23. [23] B. Schaffrin, H. Toutenburg, Weighted mixed regression, ZAMM J. Appl. Math. Mech./Zeit. Angew. Math. Mech. 70, 735-738 (1990)  Zbl0714.62061

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