A spectral method for deconvolving a density

Econometric Theory

Volumn 27, Issue 3, 2011, Pages 546-581

  Carrasco, Marine ^a   Florens, Jean Pierre ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b TOULOUSE SCHOOL OF ECONOMICS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79958863579     PISSN: 02664666     EISSN: 14694360     Source Type: Journal    
DOI: 10.1017/S026646661000040X     Document Type: Article

References (47)

1. Billingsley, P. (1995) Probability and Measure. Wiley.
2. Blundell, R., X. Chen, & D. Kristensen (2007) Semi-nonparametric IV estimation of shape-invariant Engel curves. Econometrica 75, 1613-1669.
3. Carrasco, M. & J.P. Florens (2002) Simulation based method of moments and efficiency. Journal of Business & Economic Statistics 20(4), 482-492.
4. Carrasco, M., J.P. Florens, & E. Renault (2007) Linear inverse problems in structural econometrics: Estimation based on spectral decomposition and regularization. In J.J. Heckman & E.E. Leamer (eds.), The Handbook of Econometrics, vol. 6, pp. 5633-5751. Elsevier.
5. Carroll, R. & P. Hall (1988) Optimal rates of convergence for deconvolving a density. Journal of American Statistical Association 83(404), 1184-1186.
6. Carroll, R. & P. Hall (2004) Low order approximations in deconvolution and regression with errors in variables. Journal of the Royal Statistical Society Series B 66, 31-46. (Pubitemid 38203119)
7. Carroll, R., A. Van Rooij, & F. Ruymgaart (1991) Theoretical aspects of iii-posed problems in statistics. Acta Applicandae Mathematicae 24, 113-140.
8. Chernozhukov V., P. Gagliardini, & O. Scaillet (2008) Nonparametric Instrumental Variable, Estimation of Quantile Structural Effects. Working paper, Swiss Finance Institute.
9. Devroye, L. (1986) Non-Uniform Random Variate Generation. Springer Verlag.
10. Devroye, L. (1989) Consistent deconvolution in density estimation. Canadian Journal of Statistics 17, 235-239.
11. Donoho, D. (1995) Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Applied and Computational Harmonic Analysis 2, 101-126.
12. Dunford, N. & J. Schwartz (1963) Linear Operators, Part II, Spectral Theory. Wiley.
13. Efromovich (1997) Density estimation for the case of supersmooth measurement error. Journal of the American Statistical Association 92(438), 526-535.
14. Engl. H.W., M. Hanke, & A. Neubauer (1996) Regularization of Inverse Problems. Kluwer Academic.
15. Fan, J. (1991a) On the optimal rates of convergence for nonparametric deconvolution problems. Annals of Statistics 19, 1257-1272.
16. Fan, J. (1991b) Asymptotic normality for deconvolution kernel density estimators. Sankhya 53, 97-110.
17. Fan, J. (1993) Adaptively local one-dimentional subproblems with application to a deconvolution problem. Annals of Statistics 21, 600-610.
18. Gautier, E. & Y. Kitamura (2008) Nonparametric Estimation in Random Coefficients Binary Choice Models. Manuscript, Yale University.
19. Geweke, J. (1988) Antithetic acceleration of Monte Carlo integration in Bayesian inference. Journal of Econometrics 38, 73-90.
20. Gourieroux, C. & A. Monfort (1996) Simulation-Based Econometric Methods. Oxford University Press.
21. Groeneboom, P. & G. Jongbloed (2003) Density estimation in the uniform deconvolution model. Statistica Neerlandica 57, 136-157. (Pubitemid 41724442)
22. Hall, P. & J. Horowitz (2005) Nonparametric methods for inference in the presence of instrumental variables. Annals of Statistics 33, 2904-2929. (Pubitemid 43384880)
23. Hall, P. & A. Meister (2007) A ridge-parameter approach to deconvolution. Annals of Statistics 35, 1535-1558.
24. Hall, P., F. Ruymgaart, O. van Gaans, & A. van Rooij (2001) Inverting noisy integral equations using wavelet expansions: A class of irregular convolutions. In M.C.M. de Gunst, C.A.J. Klassen, & A.W. van der Vaart (eds.), Festschrift in Honor of Willem van Zwet. IMS Lectures Notes Monograph Series, vol. 36, pp. 533-546. Institute of Mathematical Statistics.
25. Horowitz, J. & M. Markatou (1996) Semiparametric estimation of regression models for panel data. Review of Economic Studies 63, 145-168. (Pubitemid 126458603)
26. Hu, Y. & G. Ridder (2007) Estimation of Nonlinear Models with Mismeasured Regressors Using Marginal Information. Mimeo, University of Southern California.
27. Ichimura, H. & T.S. Thompson (1998) Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution. Journal of Econometrics 86, 269-295. (Pubitemid 128413591)
28. Johannes, J. (2009) Deconvolution with unknown error distribution. Annals of Statistics 39, 2301-2323.
29. Johnstone, I., G. Kerkyacharian, D. Picard, & M. Raimondo (2004) Wavelet decomposition in a periodic setting. Journal of the Royal Statistical Society Series B, 66, 547-573.
30. Johnstone, I. & M. Raimondo (2004) Periodic boxcar deconvolution and diophantine approximation. Annals of Statistics 32, 1781-1804. (Pubitemid 41250250)
31. Kress, R. (1999) Linear Integral Equations. Springer.
32. Lukacs, E. (1970) Characteristic Functions. Statistical Monographs and Courses. Griffin.
33. Meister, A. (2007) Deconvolving compactly supported densities. Mathematical Methods of Statistics 16, 63-76.
34. Meister, A. (2008) Deconvolving from Fourier-oscillating error densities under decay and smoothness restrictions. Inverse Problems 24, 1-14.
35. Nashed, M.Z. & G. Wahba (1974) Generalized inverses in reproducing kernel spaces: An approach to regularization of linear operator equations. SIAM Journal on Mathematical Analysis 5, 974-987.
36. Neubauer, A. (1987) Finite-dimensional approaximation of constrained Tikhonov-regularized solutions of iii-posed linear operator equations. Mathematics of Computation 48, 565-583.
37. Neumann, M. (2007) Deconvolution from panel data with unknown error distribution. Journal of Multivariate Analysis 98, 1955-1968.
38. Pensky, M. & B. Vidakovic (1999) Adaptive wavelet estimator for nonparametric dendity deconvolution. Annals of Statistics 27, 2033-2053.
39. Postel-Vinay, F. & J.-M. Robin (2002) Equilibrium wage dispersion with worker and employer heterogeneity. Econometrica 70, 2295-2350. (Pubitemid 35384937)
40. Serfling, R. (1980) Approximation Theorems of Mathematical Statistics. Wiley.
41. Stefanski, L. & R. Carroll (1990) Deconvoluting kernel density estimators. Statistics 2, 169-184.
42. Tikhonov, A. & V. Arsenin (1977) Solutions of Ill-posed Problems. Winston & Sons.
43. Ushakov, N. (1999) Selected Topics in Characteristic Functions. VSP.
44. Van Rooij, A.C.M. & F.H. Ruymgaart (1991) Regularized deconvolution on the circle and the sphere.In G. Roussas (ed.), Nonparametric Functional Estimation and Related Topics, pp. 679-690. Kluwer Academic.
45. Van Rooij, A.C.M. & F.H. Ruymgaart (1999) On inverse estimation. In S. Ghosh (ed.), Asymptotics, Nonparametrics and Time Series, pp. 579-613. Dekker.
46. Walter, G. (1981) Orthogonal series estimators of the prior distribution. Sankhia: The Indian Journal of Statistics Series A 43, 228-245.
47. Wand, M.P. & M.C. Jones (1995) Kernel Smoothing, Chapman and Hall.