JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Robustness, Data Analysis, and Statistical Modeling: The First 50 Years and Beyond
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Robustness, Data Analysis, and Statistical Modeling: The First 50 Years and Beyond
Barrios, Erniel B.;
  PDF(new window)
 Abstract
We present a survey of contributions that defined the nature and extent of robust statistics for the last 50 years. From the pioneering work of Tukey, Huber, and Hampel that focused on robust location parameter estimation, we presented various generalizations of these estimation procedures that cover a wide variety of models and data analysis methods. Among these extensions, we present linear models, clustered and dependent observations, times series data, binary and discrete data, models for spatial data, nonparametric methods, and forward search methods for outliers. We also present the current interest in robust statistics and conclude with suggestions on the possible future direction of this area for statistical science.
 Keywords
clustered data;forward search algorithm;influence curve;L-Estimator;location parameter;M-estimator;quantile regression;R-estimator;robust statistics;spatial analysis;time series data;
 Language
English
 Cited by
 References
1.
Alhamzawi, R. (2015). Model selection in quantile regression models, Journal of Applied Statistics, 42, 445-458. crossref(new window)

2.
Atkinson, A. C. (1994). Fast very robust methods for the detection of multiple outliers, Journal of the American Statistical Association, 89, 1329-1339. crossref(new window)

3.
Atkinson, A. C. (2009). Econometric applications of the forward search in regression: Robustness, diagnostics, and graphics, Econometric Reviews, 28, 21-39.

4.
Atkinson, A. C. and Cheng, T. C. (2000). On robust linear regression with incomplete data, Computational Statistics & Data Analysis, 33, 361-380. crossref(new window)

5.
Atkinson, A. C. and Riani, M. (2007a). Exploratory tools for clustering multivariate data, Computational Statistics & Data Analysis, 52, 272-285. crossref(new window)

6.
Atkinson, A. C. and Riani, M. (2007b). Building regression models with the forward search, Journal of Computing and Information Technology, 15, 287-294. crossref(new window)

7.
Bastero, R. F. and Barrios, E. B. (2011). Robust estimation of a spatiotemporal model with structural change, Communications in Statistics-Simulation and Computation, 40, 448-468. crossref(new window)

8.
Beran, R. (1982). Robust estimation in models for independent non-identically distributed data, The Annals of Statistics, 10, 415-428. crossref(new window)

9.
Bertaccini, B. and Varriale, R. (2007). Robust analysis of variance: An approach based on the forward search, Computational Statistics & Data Analysis, 51, 5172-5183. crossref(new window)

10.
Campano, W. Q. and Barrios, E. B. (2011). Robust estimation of a time series model with structural change, Journal of Statistical Computation and Simulation, 81, 909-927. crossref(new window)

11.
Cantoni, E. and Ronchetti, E. (2001). Robust inference for generalized linear models, Journal of the American Statistical Association, 96, 1022-1030. crossref(new window)

12.
Cao, F., Ye, H. and Wang, D. (2015). A probabilistic learning algorithm for robust modeling using neural networks with random weights, information sciences, 313, 62-78. crossref(new window)

13.
Carroll, R. J. and Ruppert, D. (1982). Robust estimation in heteroscedastic linear models, The Annals of Statistics, 10, 429-441. crossref(new window)

14.
Chang, L., Hu, B., Chang, G. and Li, A. (2013). Robust derivative-free Kalman filter based on Huber's M-estimation, Journal of Process Control, 23, 1555-1561. crossref(new window)

15.
Cizek, P. (2008). Robust and efficient adaptive estimation of binary-choice regression models, Journal of the American Statistical Association, 103, 687-696. crossref(new window)

16.
Cizek, P. (2012). Semiparametric robust estimation of truncated and censored regression models, Journal of Econometrics, 168, 347-366. crossref(new window)

17.
Cressie, N. and Hawkins, D. M. (1980). Robust estimation of the variogram: I, Mathematical Geology, 12, 115-125. crossref(new window)

18.
Dang, V. A., Kim, M. and Shin, Y. (2015). In search of robust methods for dynamic panel data models in empirical corporate finance, Journal of Banking & Finance, 53, 84-98. crossref(new window)

19.
de Luna, X. and Genton, M. G. (2001). Robust simulation-based estimation of ARMA models, Journal of Computational and Graphical Statistics, 10, 370-387. crossref(new window)

20.
Dogan, O. and Taspinar, S. (2014). Spatial autoregressive models with unknown heteroscedasticity: A comparison of Bayesian and robust GMM approach, Regional Science and Urban Economics, 45, 1-21. crossref(new window)

21.
Field, C. A., Pang, Z. and Welsh, A. H. (2010). Bootstrapping robust estimates for clustered data, Journal of the American Statistical Association, 105, 1606-1616. crossref(new window)

22.
Furno, M. (2004). ARCH tests and quantile regressions, Journal of Statistical Computation and Simulation, 74, 277-292. crossref(new window)

23.
Gaglianone, W. P., Lima, L. R., Linton, O. and Smith, D. R. (2011). Evaluating value-at-risk models via quantile regression, Journal of Business & Economic Statistics, 29, 150-160. crossref(new window)

24.
Hampel, F. R. (1971). A general qualitative definition of robustness, The Annals of Mathematical Statistics, 42, 1887-1896. crossref(new window)

25.
Hampel, F. R. (1973). Robust estimation: A condensed partial survey, Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete, 27, 87-104. crossref(new window)

26.
Hampel, F. R. (1974). The influence curve and its role in robust estimation, Journal of the American Statistical Association, 69, 383-393. crossref(new window)

27.
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions, John Wiley & Sons, New York.

28.
Hardle, W. (1984). Robust regression function estimation, Journal of Multivariate Analysis, 14, 169-180. crossref(new window)

29.
Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models, Chapman and Hall, London.

30.
He, X. and Zhu, L. X. (2003). A lack-of-fit test for quantile regression, Journal of the American Statistical Association, 98, 1013-1022. crossref(new window)

31.
He, X., Fung, W. Z. and Zhu, Z. (2005). Robust estimation in generalized partial linear models for clustered data, Journal of the American Statistical Association, 100, 1176-1184. crossref(new window)

32.
Hettmansperger, T. P. and McKean, J. W. (1988). Robust Nonparametric Statistical Methods, Arnold, London.

33.
Hettmansperger, T. P., McKean, J. W., and Sheather, S. J. (2000). Robust nonparametric methods, Journal of the American Statistical Association, 95, 1308-1312. crossref(new window)

34.
Hoshino, T. (2014). Quantile regression estimation of partially linear additive models, Journal of Nonparametric Statistics, 26, 509-536. crossref(new window)

35.
Huang, A. Y. H. (2012). Volatility forecasting by quantile regression, Applied Economics, 44, 423-433. crossref(new window)

36.
Huber, P. J. (1964). Robust estimation of a location parameter, The Annals of Mathematical Statistics, 35, 73-101. crossref(new window)

37.
Huber, P. J. (1972). The 1972 wald lecture robust statistics: A review, The Annals of Mathematical Statistics, 43, 1041-1067. crossref(new window)

38.
Huber, P. J. (1973). Robust regression: Asymptotics, conjectures and Monte Carlo, The Annals of Statistics, 1, 799-821. crossref(new window)

39.
Huber, P. J. (2002). John W. Tukey's contributions to robust statistics, The Annals of Statistics, 30, 1640-1648. crossref(new window)

40.
Huber, P. J. and Ronchetti, E. M. (2009). Robust Statistics, 2nd ed., John Wiley and Sons, New York.

41.
Hubert, M. and Rousseeuw, P. J. (1997). Robust regression with both continuous and binary regressors, Journal of Statistical Planning and Inference, 57, 153-163. crossref(new window)

42.
Hung, K. W. and Siu, W. C. (2015). Learning-based image interpolation via robust k-NN searching for coherent AR parameters estimation, Journal of Visual Communication Image Representation, 31, 305-311. crossref(new window)

43.
Karunamuni, R. J., Tang, Q. and Zhao, B. (2015). Robust and efficient estimation of effective dose, Computational Statistics & Data Analysis, 90, 47-60. crossref(new window)

44.
Kelly, G. E. and Lindsey, J. K. (2002). Robust estimation of the median lethal dose, Journal of Biopharmaceutical Statistics, 12, 137-147. crossref(new window)

45.
Kitromilidou, S. and Fokianos, K. (2015). Robust estimation methods for a class of log-linear count time series models, Journal of Statistical Computation and Simulation, DOI: 10.1080/00949655.2015.1035271. crossref(new window)

46.
Kim, M. O. and Yang, Y. (2011). Semiparametric approach to a random effects quantile regression, Journal of the American Statistical Association, 106, 1405-1417. crossref(new window)

47.
Li, Y. and Zhu, J. (2008). L1-norm quantile regression, Journal of Computational and Graphical Statistics, 17, 163-185. crossref(new window)

48.
Lv, Z., Zhu, H. and Yu, K. (2014). Robust variable selection for nonlinear models with diverging number of parameters, Statistics & Probability Letters, 91, 90-97. crossref(new window)

49.
Mann, H. B. and Wald, A. (1942). On the choice of the number of class intervals in the application of the chi square test, The Annals of Mathematical Statistics, 13, 306-317. crossref(new window)

50.
Maronna, R. A. and Zamar, R. H. (2002). Robust estimates of location and dispersion for high dimensional datasets, Technometrics, 44, 307-317. crossref(new window)

51.
Mavridis, D. and Moustaki, I. (2009). The forward search algorithm for detecting response patterns in factor analysis for binary data, Journal of Computational and Graphical Statistics, 18, 1016-1034. crossref(new window)

52.
Moscone, F. and Tosetti, E. (2015). Robust estimation under error cross section dependence, Economics Letters, 133, 100-104. crossref(new window)

53.
Nassiri, V. and Loris, I. (2013). A generalized quantile regression model, Journal of Applied Statistics, 40, 1090-1105. crossref(new window)

54.
Perez, B., Molina, I. and Pena, D. (2014). Outlier detection and robust estimation in linear regression models with fixed group effects, Journal of Statistical Computation and Simulation, 84, 2652-2669. crossref(new window)

55.
Riani, M. (2004). Extensions of the forward search to time series, Studies in Nonlinear Dynamics & Econometrics, 8, Article 2.

56.
Rieder, H. (1996). Robust Statistics, Data Analysis, and Computer Intensive Methods, Springer-Verlag, New York.

57.
Sacks, J. and Ylvisaker, D. (1972). A note of Huber's robust estimation of a location parameter, The Annals of Mathematical Statistics, 43, 1068-1075. crossref(new window)

58.
Santos, K. C. P. and Barrios, E. B. (2015). Improving predictive accuracy of logistic regression model using ranked set samples, Communications in Statistics-Simulation and Computation, DOI: 10.1080/03610918.2014.955113. crossref(new window)

59.
Shahriari, H. and Ahmadi, O. (2015). Robust estimation of the mean vector for high-dimensional data set using robust clustering, Journal of Applied Statistics, 42, 1183-1205. crossref(new window)

60.
Tukey, J. W. (1962). The future of data analysis, The Annals of Mathematical Statistics, 33, 1-67. crossref(new window)

61.
Ursu, E. and Pereau, J. C. (2014). Robust modelling of periodic vector autoregressive time series, Journal of Statistical Planning and Inference, 155, 93-106. crossref(new window)

62.
Vretos, N., Tefas, A. and Pitas, I. (2013). Using robust dispersion estimation in support vector machines, Pattern Recognition, 46, 3441-3451. crossref(new window)

63.
Wang, Y., Fan, Y., Bhatt, P. and Davatzikos, C. (2010). High-dimensional pattern regression using machine learning: From medical images to continuous clinical variables, Neuroimage, 50, 1519-1535. crossref(new window)

64.
Wei, Y. and Carroll, R. J. (2009). Quantile regression with measurement error, Journal of American Statistical Association, 104, 1129-1143. crossref(new window)

65.
Wong, R. K.W., Yao, F. and Lee, T. C. M. (2014). Robust estimation for generalized additive models, Journal of Computational and Graphical Statistics, 23, 270-289. crossref(new window)

66.
Xiao, Z. (2012). Robust inference in nonstationary time series models, Journal of Econometrics, 169, 211-223. crossref(new window)

67.
Zhao, J. and Wang, J. (2009). Robust testing procedures in heteroscedastic linear models, Communications in Statistics-Simulation and Computation, 38, 244-256. crossref(new window)