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2016 | 4 | 1 | 225-232
Tytuł artykułu

Sensitivity analysis in linear models

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
225-232
Opis fizyczny
Daty
otrzymano
2015-08-09
zaakceptowano
2016-04-19
online
2016-05-02
Twórcy
  • Faculty of Education, Science, Technology and Mathematics, University of Canberra, Australia
autor
  • School of Statistics, Southwestern University of Finance and Economics, China
autor
  • School of Business Information, Shanghai University of International Business and Economics, China
Bibliografia
  • [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]
  • [2] R. D. Cook, Influential observations in linear regression, J. Amer. Statist. Assoc. 74, 169–74 (1979) [Crossref]
  • [3] R. D. Cook, Assessment of local influence (with discussion), J. Royal Statist. Soc. Ser. B 48, 133-169 (1986)
  • [4] K. T. Fang, S. Kotz, S., K. W. Ng, Symmetric Multivariate and Related Distributions (Chapman, London, 1990)
  • [5] K. T. Fang, Y. T. Zhang, Generalized Multivariate Analysis (Springer, Berlin, 1990)
  • [6] M. H. J. Gruber, Regression Estimators: A Comparative Study (John Hopkins University Press, Baltimore, MD, 2010)
  • [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]
  • [8] T. Kollo, D. von Rosen, Advanced Multivariate Statistics with Matrices (Springer, Dordrecht, 2005)
  • [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] S. Liu, Contributions to Matrix Calculus and Applications in Econometrics (Thesis Publishers, Amsterdam, 1995)
  • [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] 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] S. Liu, H. Neudecker, Local sensitivity of the restricted least squares estimator in the linear model, Statist. Pap. 48, 525 (2007)
  • [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]
  • [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] J. R.Magnus, H. Neudecker,Matrix Differential Calculus with Applications in Statistics and Econometrics (Wiley, Chichester, 1999)
  • [17] J. R. Magnus, A. L. Vasnev, Local sensitivity and diagnostic tests, Econometrics J. 10(1), 166-192 (2007)
  • [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]
  • [19] W. Polasek, Regression diagnostics for general linear regression models, J. Amer. Statist. Assoc. 79, 336-340 (1984) [Crossref]
  • [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] S. Puntanen, G. P. H. Styan, J. Isotalo,Matrix Tricks for Linear Statistical Models – Our Personal Top Twenty (Springer, Berlin, 2011)
  • [22] C. R. Rao, H. Toutenburg, Shalabh, C. Heumann, Linear Models and Generalizations (Springer, Berlin, 2008)
  • [23] B. Schaffrin, H. Toutenburg, Weighted mixed regression, ZAMM J. Appl. Math. Mech./Zeit. Angew. Math. Mech. 70, 735-738 (1990)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0021
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