Variable selection for partially linear models with measurement errors

Journal of the American Statistical Association

Volumn 104, Issue 485, 2009, Pages 234-248

  Liang, Hua ^a   Li, Runze ^b  

^a UNIVERSITY OF ROCHESTER   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Error free; Error prone; Errors in variable; Local linear regression; Quantile regression; Smoothly clipped absolute deviation

Indexed keywords

EID: 70350624776     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2009.0127     Document Type: Article

References (45)

1. Akaike, H. (1973), "Maximum Likelihood Identification of Gaussian Autoregressive Moving Average Models," Biometrika, 60, 255-265.
2. Bellman, R. (1961), Adaptive Control Processes: A Guided Tour, Princeton, NJ: Princeton University Press.
3. Berger, J., and Percchi, L. (1996), "The Intrinsic Bayes Factor for Model Selection and Prediction," Journal of the American Statistical Association, 91, 109-122.
4. Breiman, L. (1996), "Heuristics of Instability and Stabilization in Model Selection," The Annals of Statistics, 24, 2350-2383.
5. Bunea, F. (2004), "Consistent Covariate Selection and Post Model Selection Inference in SemiparametricRegression," TheAnnals of Statistics, 32, 898-927.
6. Bunea, F., and Wegkamp, M. (2004), "Two-stageModel Selection Procedures in Partially Linear Regression," The Canadian Journal of Statistics, 32, 105-118.
7. Candes, E., and Tao, T. (2007), "The Dantzig Selector: Statistical Estimation When p is Much Larger Than n" (with discussion)," The Annals of Statistics, 35, 2313-2404.
8. Carroll, R. J., Freedman, L. S., Kipnis, V., and Li, L. (1998), "A New Class of Measurement Error Models, With Applications to Estimating the Distribution of Usual Intake," The Canadian Journal of Statistics, 26, 467-477.
9. Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006), MeasurementError inNonlinearModels (2nd ed),NewYork:Chapmanand Hall.
10. Cheng, C. L., and Van Ness, J. W. (1999), Statistical Regression With Measurement Error, New York: Oxford University Press Inc.
11. Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, New York: Chapman and Hall.
12. Fan, J., and Li, R. (2001), "Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties," Journal of the American Statistical Association, 96, 1348-1360.
13. - (2004), "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, 99, 710-723.
14. Fan, J., and Lv, J. (2008), "Sure Independence Screening for Ultra-High Dimensional Feature Space" (with discussions)," Journal of the Royal Statistical Society, Ser. B., 70, 849-911.
15. Fang, K. T., Kotz, S., and Ng, K. W. (1990), Symmetric Multivariate and Related Distributions, London: Chapman and Hall.
16. Foster, D. P., and George, E. I. (1994), "The Risk Inflation Criterion for Multiple Regression," The Annals of Statistics, 22, 1947-1975.
17. Frank, I. E., and Friedman, J. H. (1993), "A Statistical View of Some Chemometrics Regression Tools," Technometrics, 35, 109-148.
18. Fuller, W. A. (1987), Measurement Error Models, New York: John Wiley.
19. George, E. I., and McCulloch, R. E. (1993), "Variable Selection via Gibbs Sampling," Journal of the American Statistical Association, 88, 881-889.
20. Gleser, L. J. (1992), "The Importance of Assessing Measurement Reliability in Multivariate Regression," Journal of the American Statistical Association, 419, 696-707.
21. He, X., and Liang, H. (2000), "Quantile Regression Estimates for a Class of Linear and Partially Linear Errors-in-Variables Models," Statistica Sinica, 10, 129-140.
22. He, X., and Shao, Q. (1996), "A General Bahadur Representation of Mestimators and Its Application to Linear Regression With Nonstochastic Designs," The Annals of Statistics, 24, 2608-2630.
23. Hocking, R. R. (1976), "The Analysis and Selection of Variables in Linear Regression," Biometrics, 32, 1-49.
24. Hoeting, J. A., Madigan, D., Raftery, A. E., and Volinsky, C. T. (1999), "Bayesian Model Averaging: A Tutorial," Statistical Science, 14, 382-417.
25. Hunter, D. R., and Lange, K. (2000), "Quantile Regression via an MM Algorithm," Journal of Computational and Graphical Statistics, 9, 60-77.
26. Hunter, D., and Li, R. (2005), "Variable Selection UsingMMAlgorithms," The Annals of Statistics, 33, 1617-1642.
27. Jiang, W. X. (2007), "Bayesian Variable Selection for High Dimensional Generalized Linear Models: Convergence Rates for the Fitted Densities," The Annals of Statistics, 35, 1487-1511.
28. Koenker, R. (2005),QuantileRegression,NewYork:CambridgeUniversity Press.
29. Li, R., Fang, K. T., and Zhu, L. X. (1997), "Some Probability Plots to Test Spherical and Elliptical Symmetry," Journal of Computational and Graphical Statistics, 6, 435-450.
30. Liang, H., Härdle, W., and Carroll, R. J. (1999), "Estimation in a Semiparametric Partially Linear Errors-in-Variables Model," The Annals of Statistics, 27, 1519-1935.
31. Liang, H., and Li, R. (2008): "Variable Selection for Partially Linear Models With Measurement Errors." Technical Report. Department of Biostatistics, University of Rochester Medical Center, Rochester, NY.
32. Liang, H.,Wang, S. J., and Carroll, R. J. (2007), "Partially Linear ModelsWith Missing Response Variables and Error-prone Covariates," Biometrika, 94, 185-198.
33. Lindley, D. B. (1947), "Regression Lines and the Functional Relationship," Journal of the Royal Statistical Society, Ser. B, 9, 219-244.
34. Ma, Y. Y., and Carroll, R. J. (2006), "Locally Efficient Estimators for Semiparametric Models With Measurement Error," Journal of the American Statistical Association, 101, 1465-1474.
35. Mack, Y., and Silverman, B. (1982), "Weak and Strong Uniform Consistency of Kernel Regression Estimates," Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 60, 405-415.
36. Madansky, A. (1959), "The Fitting of Straight Lines When Both Variables Are Subject toError," Journal of theAmerican StatisticalAssociation, 54, 173-205.
37. Mitchell, T. J., and Beauchamp, J. J. (1988), "Bayesian Variable Selection in Linear Regression," Journal of the American Statistical Association, 83, 1023-1032.
38. Newey, W. K. (1994), "The Asymptotic Variance of Semiparametric Estimators," Econometrica, 62, 1349-1382.
39. Pan,W. Q., Zeng, D. L., and Lin, X. H. (2008), "Estimation in Semiparametric Transition Measurement Error Models for Longitudinal Data," Biometrics., forthcoming in.
40. Raftery, A. E., Madigan, D., and Hoeting, J. A. (1997), "Bayesian Model Averaging for Linear Regression Models," Journal of the American Statistical Association, 92, 179-191.
41. Ruppert, D., Sheather, S. J., and Wand, M. P. (1995), "An Effective Bandwidth Selector for Local Least Squares Regression," Journal of the American Statistical Association, 90, 1257-1270.
42. Schwarz, G. (1978), "Estimating the Dimension of a Model," The Annals of Statistics, 6, 461-464.
43. Tibshirani, R. (1996), "Regression Shrinkage and Selection via the LASSO," Journal of the Royal Statistical Society, Ser. B, 58, 267-288.
44. Wang, H., Li, R., and Tsai, C. L. (2007), "Tuning Parameter Selectors for the Smoothly Clipped Absolute Deviation Method," Biometrika, 94, 553-568.
45. Wang, N. S., Lin, X.H.,Gutierrez,R.G., and Carroll,R. J. (1998), "BiasAnalysis and SIMEX Approach in Generalized Linear Mixed Measurement Error Models," Journal of the American Statistical Association, 93, 249-261.