Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics

We propose an influence diagnostic methodology for linear regression models with stochastic restrictions and errors following elliptically contoured distributions. We study how a perturbation may impact on the mixed estimation procedure of parameters in the model. Normal curvatures and slopes for assessing influence under usual schemes are derived, including perturbations of case-weight, response variable, and explanatory variable. Simulations are conducted to evaluate the performance of the proposed methodology. An example with real-world economy data is presented as an illustration.

[1]  R. Cook.  Assessment of Local Influence , 1986 .

[2]  Shuangzhe Liu,et al.  Local influence in multivariate elliptical linear regression models , 2002 .

[3]  S. Chatterjee.  Sensitivity analysis in linear regression , 1988 .

[4]  Gilberto A. Paula,et al.  Influence Diagnostics in log-Birnbaum-Saunders Regression Models , 2004 .

[5]  A. Atkinson.  Econometric Applications of the Forward Search in Regression: Robustness, Diagnostics, and Graphics , 2008 .

[6]  Gilberto A. Paula,et al.  Robust statistical modeling using the Birnbaum-Saunders- t distribution applied to insurance , 2012 .

[7]  C. Heyde,et al.  On estimation in conditional heteroskedastic time series models under non-normal distributions , 2008 .

[8]  Hu Yang,et al.  A new stochastic mixed ridge estimator in linear regression model , 2010 .

[9]  Heleno Bolfarine,et al.  Local influence in elliptical linear regression models , 1997 .

[10]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[11]  Shuangzhe Liu,et al.  On local influence for elliptical linear models , 2000 .

[12]  J. A. Díaz-García,et al.  SINGULAR ELLIPTICAL DISTRIBUTION: DENSITY AND APPLICATIONS , 2002 .

[13]  Helton Saulo,et al.  A family of autoregressive conditional duration models applied to financial data , 2014, Comput. Stat. Data Anal..

[14]  Gilberto A. Paula,et al.  Restricted methods in symmetrical linear regression models , 2005, Comput. Stat. Data Anal..

[15]  Lei Shi,et al.  Local influence in principal components analysis , 1997 .

[16]  Manuel González,et al.  Influence diagnostics in the tobit censored response model , 2010, Stat. Methods Appl..

[17]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[18]  Shuangzhe Liu,et al.  On diagnostics in conditionally heteroskedastic time series models under elliptical distributions , 2004, Journal of Applied Probability.

[19]  H. Theil,et al.  Testing the Independence of Regression Disturbances , 1961 .

[20]  J. A. Díaz-García,et al.  SENSITIVITY ANALYSIS IN LINEAR REGRESSION , 2022 .

[21]  John Haslett,et al.  Application of ‘delete = replace’ to deletion diagnostics for variance component estimation in the linear mixed model , 2004 .

[22]  H. Neudecker,et al.  Solution of Problem 1/SP07: Local Sensitivity of the Restricted Least Squares Estimator in the Linear Model , 2007 .

[23]  Manuel Galea,et al.  Diagnostics in Birnbaum-Saunders accelerated life models with an application to fatigue data , 2014 .

[24]  A. Goldberger,et al.  On Pure and Mixed Statistical Estimation in Economics , 1961 .

[25]  Filidor V. Vilca,et al.  Influence analysis in skew-Birnbaum–Saunders regression models and applications , 2011 .

[26]  Víctor Leiva,et al.  Birnbaum–Saunders statistical modelling: a new approach , 2014 .

[27]  J. Durbin.  A Note on Regression When There is Extraneous Information About One of the Coefficients , 1953 .

[28]  Hu Yang,et al.  Performances of the Positive-Rule Stein-Type Ridge Estimator in a Linear Regression Model with Spherically Symmetric Error Distributions , 2013 .

[29]  C. Heyde,et al.  Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models , 2011 .

[30]  José A. Díaz-García,et al.  Influence Diagnostics for Elliptical Multivariate Linear Regression Models , 2003 .

[31]  An Application of the Local Influence Diagnostics to Ridge Regression Under Elliptical Model , 2007 .

[32]  Cristian Villegas,et al.  Birnbaum-Saunders Mixed Models for Censored Reliability Data Analysis , 2011, IEEE Transactions on Reliability.

[33]  Gilberto A. Paula,et al.  On diagnostics in symmetrical nonlinear models , 2005 .

[34]  Wolfgang Polasek,et al.  The Hadamard Product and Some of its Applications in Statistics , 1995 .

[35]  B. Efron,et al.  Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information , 1978 .

[36]  Manuel Galea,et al.  Influence diagnostics on the coefficient of variation of elliptically contoured distributions , 2011 .

[37]  Luis Hernando Vanegas,et al.  Assessing Robustness of Inference in Symmetrical Nonlinear Regression Models , 2013 .

[38]  Frederik P. Agterberg.  Regression Estimators; A Comparative Study: by Marvin H. J. Gruber, 1990, Academic Press, Inc., Boston, xi + 347p., ISBN 0-12-304752-8, $49.95 (U.S.) , 1991 .

[39]  F. Cysneiros,et al.  Local Influence Under Parameter Constraints , 2010 .

[40]  Gilberto A. Paula,et al.  Assessing local influence in restricted regression models , 1993 .

[41]  H. Theil.  On the Use of Incomplete Prior Information in Regression Analysis , 1963 .

[42]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics , 1991 .

[43]  S. Kotz,et al.  Symmetric Multivariate and Related Distributions , 1989 .

[44]  J. A. Díaz-García,et al.  Doubly Non-central t and Distributions Obtained Under Singular and Non-singular Elliptic Distributions , 2003 .

[45]  N. Billor.  An application of the local influence approach to ridge regression , 1999 .

[46]  Guy Lebanon,et al.  Linear Regression , 2010 .

[47]  Francisco José de A. Cysneiros,et al.  Assessment of diagnostic procedures in symmetrical nonlinear regression models , 2010, Comput. Stat. Data Anal..

[48]  Gilberto A. Paula,et al.  On influence diagnostic in univariate elliptical linear regression models , 2003 .

[49]  Francisco José A. Cysneiros,et al.  Residuals and their statistical properties in symmetrical nonlinear models , 2008 .

[50]  B. M. Golam Kibria,et al.  A Simulation Study on Some Restricted Ridge Regression Estimators , 2013, Commun. Stat. Simul. Comput..

[51]  S. E. Ahmed,et al.  Influence Diagnostics in the linear regression model with linear stochastic restrictions , 2009 .

[52]  Lei Shi,et al.  Local influence in ridge regression , 1999 .

[53]  R. M. Loynes,et al.  Local influence: a new approach , 1993 .