Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information

REFERENCES

• Barnett , S. A. and Sakellaris , P. 1998 . “Nonlinear Response of Firm Investment to Q: Testing a Model of Convex and Non-Convex Adjustment Costs,” . Journal of Monetary Economics , 42 : 261 – 288 .
   Web of Science ®Google Scholar
• Bauer , D. J. 2005 . “The Role of Nonlinear Factor-to-Indicator Relationships in Tests of Measurement Equivalence,” . Psychological Methods , 10 : 305 – 316 .
   PubMed Web of Science ®Google Scholar
• Beckmann , C. F. and Smith , S. M. 2004 . “Probabilistic Independent Component Analysis for Functional Magnetic Resonance Imaging,” . IEEE Transactions on Medical Imaging , 23 : 137 – 152 .
   PubMed Web of Science ®Google Scholar
• Bickel , P. J. and Freedman , D. A. 1981 . “Some Asymptotic Theory for the Bootstrap,” . The Annals of Statistics , 9 : 1196 – 1217 .
   Web of Science ®Google Scholar
• Bonhomme , S. and Robin , J.-M. 2009 . “Consistent Noisy Independent Component Analysis,” . Journal of Econometrics , 149 : 12 – 25 .
   Web of Science ®Google Scholar
• Bonhomme , S. and Robin , J.-M. 2010 . “Generalized Non-Parametric Deconvolution With an Application to Earnings Dynamics,” . Review of Economic Studies , 77 : 491 – 533 .
   Web of Science ®Google Scholar
• Brainard , W. C. and Tobin , J. 1968 . “Pitfalls in Financial Model Building,” . American Economic Review , 58 : 99 – 122 .
   Web of Science ®Google Scholar
• Cardoso , J. and Souloumiac , A. 1993 . “Blind Beamforming for Non-Gaussian Signals,” . IEE Proceedings-F , 140 : 362 – 370 .
   Google Scholar
• Carroll , R. J. , Chen , X. and Hu , Y. 2010a . “Identification and Estimation of Nonlinear Models Using Two Samples With Nonclassical Measurement Errors,” . Journal of Nonparametric Statistics , 22 : 379 – 399 .
   PubMed Web of Science ®Google Scholar
• Carroll , R. J. , Chen , X. and Hu , Y. 2010b . “Rejoinder: Identification and Estimation of Nonlinear Models Using Two Samples With Nonclassical Measurement Errors,” . Journal of Nonparametric Statistics , 22 : 419 – 423 .
   Web of Science ®Google Scholar
• Carroll , R. J. , Ruppert , D. , Stefanski , L. A. and Crainiceanu , C. M. 2006 . Measurement Error in Nonlinear Models , New York : Chapman and Hall .
   Google Scholar
• Chen , Q. X. and Ibrahim , D. L. Z. J. G. 2007 . “Sieve Maximum Likelihood Estimation for Regression Models With Covariates Missing at Random,” . Journal of the American Statistical Association , 102 : 1309 – 1317 .
   Web of Science ®Google Scholar
• Chen , X. , Hu , Y. and Lewbel , A. 2009 . “Nonparametric Identification and Estimation of Nonclassical Errors-in-Variables Models Without Additional Information,” . Statistica Sinica , 19 : 949 – 968 .
   Web of Science ®Google Scholar
• Chesher , A. 1991 . “The Effect of Measurement Error,” . Biometrika , 78 : 451 – 462 .
   Web of Science ®Google Scholar
• Chesher , A. 1998 . “Polynomial Regression With Normal Covariate Measurement Error,” . Discussion Paper 98/448, University of Bristol
   Google Scholar
• Cragg , J. C. 1997 . “Using Higher Moments to Estimate the Simple Errors-in-Variables Model,” . Rand Journal of Economics , 28 : S71 – S91 .
   Web of Science ®Google Scholar
• Dagenais , M. G. and Dagenais , D. L. 1997 . “Higher Moment Estimators for Linear Regression Models With Errors in Variables,” . Journal of Econometrics , 76 : 193 – 221 .
   Web of Science ®Google Scholar
• Erickson , T. and Whited , T. M. 2000 . “Measurement Error and the Relationship Between Investment and ‘q’,” . Journal of Political Economy , 108 : 1027 – 1057 .
   Web of Science ®Google Scholar
• Erickson , T. and Whited , T. M. 2002 . “Two-Step GMM Estimation of the Errors-in-Variables Model Using High-Order Moments,” . Econometric Theory , 18 : 776 – 799 .
   Web of Science ®Google Scholar
• Fan , J. 1991 . “On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems,” . The Annals of Statistics , 19 : 1257 – 1272 .
   Web of Science ®Google Scholar
• Fuller , W. A. 1987 . Measurement Error Models , New York : Wiley .
   Google Scholar
• Geary , R. C. 1942 . “Inherent Relations Between Random Variables,” . Proceedings of the Royal Irish Academy , 47A : 63 – 76 .
   Google Scholar
• Grunfeld , Y. 1960 . “The Determinants of Corporate Investment,” . In The Demand for Durable Goods , Edited by: Harberger , A. 211 – 266 . Chicago, , IL : University Chicago Press .
   Google Scholar
• Hausman , J. , Newey , W. , Ichimura , H. and Powell , J. 1991 . “Measurement Errors in Polynomial Regression Models,” . Journal of Econometrics , 50 : 273 – 295 .
   Web of Science ®Google Scholar
• Hu , Y. and Ridder , G. 2012 . “Estimation of Nonlinear Models with Measurement Error Using Marginal Information,” . Journal of Applied Econometrics , 27 : 347 – 385 .
   Google Scholar
• Hu , Y. and Schennach , S. M. 2008 . “Instrumental Variable Treatment of Nonclassical Measurement Error Models,” . Econometrica , 76 : 195 – 216 .
   Web of Science ®Google Scholar
• Hyvärinen , A. and Oja , E. 1997 . “A Fast Fixed Point Algorithm for Indepen- dent Component Analysis,” . Neural Computation , 9 : 1483 – 1492 .
   Web of Science ®Google Scholar
• Ikeda , S. and Toyama , K. 2000 . “Independent Component Analysis for Noisy Data—MEG Data Analysis,” . Neural Networks , 13 : 1063 – 1074 .
   PubMedGoogle Scholar
• Jutten , C. and Karhunen , J. 2003 . “Advances in Nonlinear Blind Source Separation,” . In Proceedings of the 4th International Symposium on Independent Component Analysis and Blind Signal Separation (ICA2003) 245 – 256 .
   Google Scholar
• Kapteyn , A. and Wansbeek , T. 1983 . “Identification in the Linear Errors in Variables Model,” . Econometrica , 51 : 1847 – 1849 .
   Web of Science ®Google Scholar
• Kendall , M. G. and Stuart , A. 1979 . The Advanced Theory of Statistics (4th ed.) , New York : Macmillan .
   Google Scholar
• Kenny , D. A. and Judd , C. M. 1984 . “Estimating the Nonlinear and Interactive Effects of Latent Variables,” . Psychological Bulletin , 96 : 201 – 210 .
   Web of Science ®Google Scholar
• Klepper , S. and Leamer , E. E. 1984 . “Consistent Sets of Estimates for Regre- ssions With Errors in All Variables,” . Econometrica , 52 : 163 – 183 .
   Web of Science ®Google Scholar
• Lewbel , A. 1997 . “Constructing Instruments for Regressions with Measurement Error When no Additional Data are Available, With an Application to Patents and R&D,” . Econometrica , 65 : 1201 – 1213 .
   Web of Science ®Google Scholar
• Li , T. and Vuong , Q. 1998 . “Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators,” . Journal of Multivariate Analysis , 65 : 139 – 165 .
   Web of Science ®Google Scholar
• Lukacs , E. 1970 . Characteristic Functions (2nd ed.) , London : Griffin .
   Google Scholar
• Mahajan , A. 2006 . “Identification and Estimation of Single Index Models With Misclassified Regressor,” . Econometrica , 74 : 631 – 665 .
   Web of Science ®Google Scholar
• Newey , W. 2001 . “Flexible Simulated Moment Estimation of Nonlinear Errors-in-Variables Models,” . Review of Economics and Statistics , 83 : 616 – 627 .
   Web of Science ®Google Scholar
• Nocedal , J. 1980 . “Updating Quasi-Newton Matrices With Limited Storage,” . Mathematics of Computation , 35 : 773 – 782 .
   Web of Science ®Google Scholar
• Pal , M. 1980 . “Consistent Moment Estimators of Regression-Coefficients in the Presence of Errors in Variables,” . Journal of Econometrics , 14 : 349 – 364 .
   Web of Science ®Google Scholar
• Politis , D. N. , Romano , J. P. and Wolf , M. 1999 . Subsampling , New York : Springer .
   Google Scholar
• Reiersol , O. 1950 . “Identifiability of a Linear Relation Between Variables Which are Subject to Error,” . Econometrica , 18 : 375 – 389 .
   Web of Science ®Google Scholar
• Schennach , S. M. 2004a . “Estimation of Nonlinear Models With Measurement Error,” . Econometrica , 72 : 33 – 75 .
   Web of Science ®Google Scholar
• Schennach , S. M. 2004b . “Nonparametric Estimation in the Presence of Measurement Error,” . Econometric Theory , 20 : 1046 – 1093 .
   Web of Science ®Google Scholar
• Schennach , S. M. 2007 . “Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models,” . Econometrica , 75 : 201 – 239 .
   Web of Science ®Google Scholar
• Schennach , S. M. 2009 . “Instrumental Variable Treatment of the Nonparametric Berkson Measurement Error Model,” . Working Paper, University of Chicago
   Google Scholar
• Shen , X. 1997 . “On Methods of Sieves and Penalization,” . The Annals of Statistics , 25 : 2555 – 2591 .
   Web of Science ®Google Scholar
• Tobin , J. 1969 . “A General Equilibrium Approach to Monetary Theory,” . Journal of Money Credit and Banking , 1 : 15 – 29 .
   Google Scholar
• Wang , L. and Hsiao , C. 2003 . “Identification and Estimation of Semiparametric Nonlinear Errors-in-Variables Models,” . Journal of Econometrics , 165 : 30 – 44 .
   Google Scholar
• Yalcin , I. and Amemiya , Y. 2001 . “Nonlinear Factor Analysis as a Statistical Method,” . Statistical Science , 16 : 275 – 294 .
   Google Scholar