Estimating the Model with Fixed and Random Effects by a Robust Method

详细信息    查看全文

• 作者：Jan ámos Ví?ek
• 关键词：Linear regression model ; The least weighted squares ; Fixed and random effects ; Numerical simulations ; 62J02 ; 62F35
• 刊名：Methodology and Computing in Applied Probability
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：17
• 期：4
• 页码：999-1014
• 全文大小：259 KB
• 参考文献：Amos CI (1994) Robust variance-components approach for assessing genetic linkage, in pedigrees. Am J Hum Genet 54:535-43
  Atkinson AC, Riani M (2000) Robust diagnostic regresion analysis. Springer, New YorkCrossRef
  Bickel PJ (1975) One-step Huber estimates in the linear model. JASA 70:428-33MATH MathSciNet CrossRef
  Bramati MC, Croux C (2007) Robust estimators for the fixed effects panel data model. Econ J 10:521-40MATH
  Bo?ek P, Lachout P (1993) Linear programming approach to LMS-estimation. Memorial vol Comput Statist & Data Anal 19(1995):129-34
  Balestra P, Nerlove M (1966) Source pooling cross section and time series data in the estimation of a dynamic model: The demand for natural gas. Econometrica 34:585-12CrossRef
  Cameron AC, Gelbach JB, Miller DL (2011) Robust inference with multiway clustering. J Bus & Econ Stat 29:238-49MATH MathSciNet CrossRef
  Cragg JG (1983) More efficient estimation in the presence of heteroscedasticity of unknown form. Econometrica 51:751-63MATH MathSciNet CrossRef
  Croux C, Rousseeuw PJ (1992) A class of high
  eakdown scale estimators based on subranges. Comm Statist- Theory Methods 21:1935-951MATH MathSciNet CrossRef
  Davies L (1990) The asymptotics of S-estimators in the linear regression model. Ann Statistics 18:1651-675MATH CrossRef
  Dehon C, Gassner M, Veradi V (2009) Beware of ‘good-outliers and overoptimistic conclussios. Oxford Bull Econ Statist 71:437-52CrossRef
  Fisher RA (1920) A mathematical examination of the methods of determining the accuracy of an observation by the mean error and by the mean squares error. Mon Not Roy Astr Soc 80:758-70CrossRef
  Galton F (1886) Regression towards mediocrity in hereditary stature. J Anthropol Inst 15:246-63
  Gill PS (2000) A robust mixed linear model analysis for longitudinal data. Stat Med 19:975?987CrossRef
  Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA (1986) Robust statistics -the approach based on influence functions. Wiley, New YorkMATH
  Hausman J (1978) Specification test in econometrics. Econometrica 46(1978):1251-271MATH MathSciNet CrossRef
  Hausman JA, Taylor WE (1981) Panel data and unobservable individual effects. Econometrica 49:1377-398MATH MathSciNet CrossRef
  Hettmansperger TP, Sheather SJ (1992) A cautionary note on the method of least median squares. Am Stat 46:79-3MathSciNet
  Huber PJ (1981) Robust statistics. Wiley, New YorkMATH CrossRef
  Jones DR (1992) Meta-analysis of observational epidemiological studies: A review. J R Soc Med 85:165-68
  Judge GG, Griffiths WE, Hill RC, Lutkepohl H, Lee TC (1985) The Theory and Practice of Econometrics. Wiley, New York
  Jure?ková J, Sen PK (1984) On adaptive scale-equivariant M-estimators in linear models Statistics and Decisions 2 (1984), Suppl. Issue No. 1.
  Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46:33-0MATH MathSciNet CrossRef
  Koenker R (2004) Quantile regression for longitudinal data. J Multivar Anal 91:74-9MATH MathSciNet CrossRef
  Kott P (1989) Robust small domain estimation using random effects modelling. Survey Methodology 15:1-2
  Maddala GS (1971) The use of variance components models in pooling cross section and time series data. Econometrica 39:341-58MathSciNet CrossRef
  Pinheiro JC, Liu C (2001) Efficient Algorithms for Robust Estimation, in Linear mixed-Effects models using the multivariate t-Distribution. J Comput Graph Stat 10:249-76MathSciNet CrossRef
  Portnoy S (1983) Tightness of the sequence of empiric c.d.f. processes defined from regression fractiles. In: Franke J, Ha?rdle W, Martin D (eds) Robust and nonlinear time-series analysis. Springer-Verlag, NY 1983, pp 231-46
  Rocke DM (1991) Robustness and balance in the mixed models. Biometrics 47:303-09CrossRef
  Rousseeuw PJ (1984) Least median of square regression. JASA 79:871-80MATH MathSciNet CrossRef
  Schall R (1991) Estimation in generalized linear models with random effects. Biometrika 72:593-
  ?indelá? J (1994) On L-estimators viewed as M-estimators. Kybernetika 30 (1994):5,551-62
  Telser LG (1964) Iterative Simultaneous Estimation of Sets of Linear Regressions. J Am Stat Assoc 59:845-2MATH MathSciNet CrossRef
  Veradi V, Croux C (2009) Robust regression in Stata. Stat J 9(3):439-53
  Veradi V, Wagner J (2010) Robust estimation of of linear fixed effects panel data model with an application to the exporter productivity premium Discussion paper No 4928, IZA, Bonn
  Ví?ek Já (1996) A cautionary note on the method of Least Median of Squares reconsidered Trans Twelfth Prague Conf on Inform Theory, Statist Dec Functions and Rand Proc, Academy of Sciences of the Czech Republic, pp 254-59
  Ví?ek Já (1996) Sensitivity analysis of M-estimates. Ann Inst Stat Math 48:469-95MATH CrossRef
  Ví?ek Já (1998) Robust specification test. In: Marie Hu?ková, Petr Lachout & , Jan ámos Ví?ek (eds) Proceedings of Prague Stochastics-8. Published by Union of Czecho
• 作者单位：Jan ámos Ví?ek (1)
  
  1. Faculty of Social Sciences, Institute of Economic Studies, Charles University, Opletalova 26, Prague, The Czech Republic
  
• 刊物主题：Statistics, general; Life Sciences, general; Electrical Engineering; Economics general; Business/Management Science, general;
• 出版者：Springer US
• ISSN：1573-7713

文摘

Regression model with fixed and random effects estimated by modified versions of the Ordinary Least Squares (OLS) is a standard tool of panel data analysis. However, it is vulnerable to the bad effects of influential observations (contamination and/or atypical observations). The paper offers robustified versions of the classical methods for this framework. The robustification is carried out by the same idea which was employed when robustifying OLS, it is the idea of weighting down the large order statistics of squared residuals. In contrast to the approach based on the M-estimators this approach does not need the studentization of residuals to reach the scale- and regression-equivariance of estimator in question. Moreover, such approach is not vulnerable with respect the inliers. The numerical study reveals the reliability of the respective algorithm. The results of this study were collected in a file which is possible to find on web, address is given below. Patterns of these results were included also into the paper. The possibility to reach nearly the full efficiency of estimation - due to the iteratively tailored weight function - in the case when there are no influential points is also demonstrated. Keywords Linear regression model The least weighted squares Fixed and random effects Numerical simulations