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Volumn 66, Issue 1, 2004, Pages 31-46

Low order approximations in deconvolution and regression with errors in variables

Author keywords

Density estimation; Measurement error; Nonparametric regression; Orthogonal series; Simulation extrapolation

Indexed keywords


EID: 1042267765     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2004.00430.x     Document Type: Article
Times cited : (48)

References (46)
  • 1
    • 0001736196 scopus 로고
    • Optimal rates of convergence for deconvolving a density
    • Carroll, R. J. and Hall, P. (1988) Optimal rates of convergence for deconvolving a density. J. Am. Statist. Ass., 83, 1184-1186.
    • (1988) J. Am. Statist. Ass. , vol.83 , pp. 1184-1186
    • Carroll, R.J.1    Hall, P.2
  • 2
    • 0000794498 scopus 로고    scopus 로고
    • Asymptotics for the SIMEX estimator in nonlinear measurement error models
    • Carroll, R. J., Küchenhoff, H., Lombard, F. and Stefanski, L. A. (1996) Asymptotics for the SIMEX estimator in nonlinear measurement error models. J. Am. Statist. Ass., 91, 242-250.
    • (1996) J. Am. Statist. Ass. , vol.91 , pp. 242-250
    • Carroll, R.J.1    Küchenhoff, H.2    Lombard, F.3    Stefanski, L.A.4
  • 3
    • 0001749398 scopus 로고    scopus 로고
    • Nonparametric regression with errors in covariates
    • Carroll, R. J., Maca, J. D. and Ruppert, D. (1999) Nonparametric regression with errors in covariates. Biometrika, 86, 541-554.
    • (1999) Biometrika , vol.86 , pp. 541-554
    • Carroll, R.J.1    Maca, J.D.2    Ruppert, D.3
  • 5
    • 0042910589 scopus 로고    scopus 로고
    • Deconvolution with arbitrarily smooth kernels
    • Cator, E. A. (2001) Deconvolution with arbitrarily smooth kernels. Statist. Probab. Lett., 54, 205-214.
    • (2001) Statist. Probab. Lett. , vol.54 , pp. 205-214
    • Cator, E.A.1
  • 6
    • 0034878562 scopus 로고    scopus 로고
    • Measurement errors in line transect surveys where detectability varies with distance and size
    • Chen, S. X. and Cowling, A. (2001) Measurement errors in line transect surveys where detectability varies with distance and size. Biometrics, 57, 732-742.
    • (2001) Biometrics , vol.57 , pp. 732-742
    • Chen, S.X.1    Cowling, A.2
  • 7
    • 84950936262 scopus 로고
    • Simulation-extrapolation in parametric measurement error models
    • Cook, R. J. and Stefanski, L. A. (1994) Simulation-extrapolation in parametric measurement error models. J. Am. Statist. Ass., 89, 1314-1328.
    • (1994) J. Am. Statist. Ass. , vol.89 , pp. 1314-1328
    • Cook, R.J.1    Stefanski, L.A.2
  • 8
    • 0031315250 scopus 로고    scopus 로고
    • Deconvolution of a distribution function
    • Cordy, C. B. and Thomas, D. R. (1997) Deconvolution of a distribution function. J. Am. Statist. Ass., 92, 1459-1465.
    • (1997) J. Am. Statist. Ass. , vol.92 , pp. 1459-1465
    • Cordy, C.B.1    Thomas, D.R.2
  • 9
    • 84988101319 scopus 로고
    • Consistent deconvolution in density estimation
    • Devroye, L. (1989) Consistent deconvolution in density estimation. Can. J. Statist., 17, 235-239.
    • (1989) Can. J. Statist. , vol.17 , pp. 235-239
    • Devroye, L.1
  • 10
    • 0031533944 scopus 로고    scopus 로고
    • Density estimation for the case of supersmooth measurement error
    • Efromovich, S. (1997) Density estimation for the case of supersmooth measurement error. J. Am. Statist. Ass., 92, 526-535.
    • (1997) J. Am. Statist. Ass. , vol.92 , pp. 526-535
    • Efromovich, S.1
  • 11
    • 0345856570 scopus 로고    scopus 로고
    • Multi bandwidth kernel estimators for nonparametric deconvolution problems: Asymptotics and finite sample performance
    • van Es, B. and Uh, H. W. (2000) Multi bandwidth kernel estimators for nonparametric deconvolution problems: asymptotics and finite sample performance. J. Nonparam. Statist., 13, 107-128.
    • (2000) J. Nonparam. Statist. , vol.13 , pp. 107-128
    • Van Es, B.1    Uh, H.W.2
  • 12
    • 0000867838 scopus 로고
    • On the optimal rates of convergence for nonparametric deconvolution problems
    • Fan, J. (1991) On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Statist., 19, 1257-1272.
    • (1991) Ann. Statist. , vol.19 , pp. 1257-1272
    • Fan, J.1
  • 13
    • 84988123046 scopus 로고
    • Deconvolution with supersmooth distributions
    • Fan, J. (1992) Deconvolution with supersmooth distributions. Can. J. Statist., 20, 155-169.
    • (1992) Can. J. Statist. , vol.20 , pp. 155-169
    • Fan, J.1
  • 14
    • 21344496605 scopus 로고
    • Nonparametric regression with errors in variables
    • Fan, J. and Truong, Y. (1993) Nonparametric regression with errors in variables. Ann. Statist., 21, 1900-1925.
    • (1993) Ann. Statist. , vol.21 , pp. 1900-1925
    • Fan, J.1    Truong, Y.2
  • 15
    • 0042708536 scopus 로고    scopus 로고
    • Invariance principles for deconvolving kernel density estimation for stationary sequences of random variables
    • Fotopoulos, S. B. (2000) Invariance principles for deconvolving kernel density estimation for stationary sequences of random variables. J. Statist. Planng Inf., 86, 31-50.
    • (2000) J. Statist. Planng Inf. , vol.86 , pp. 31-50
    • Fotopoulos, S.B.1
  • 16
    • 0000937636 scopus 로고    scopus 로고
    • On pointwise adaptive nonparametric deconvolution
    • Goldenshluger, A. (1999) On pointwise adaptive nonparametric deconvolution. Bernoulli, 5, 907-925.
    • (1999) Bernoulli , vol.5 , pp. 907-925
    • Goldenshluger, A.1
  • 18
    • 0008697575 scopus 로고
    • Deconvolving a density from partially contaminated observations
    • Hesse, C. H. (1995a) Deconvolving a density from partially contaminated observations. J. Multiv. Anal., 55, 246-260.
    • (1995) J. Multiv. Anal. , vol.55 , pp. 246-260
    • Hesse, C.H.1
  • 19
    • 0029427101 scopus 로고
    • Deconvolving a density from contaminated dependent observations
    • Hesse, C. H. (1995b) Deconvolving a density from contaminated dependent observations. Ann. Inst. Statist. Math., 47, 645-663.
    • (1995) Ann. Inst. Statist. Math. , vol.47 , pp. 645-663
    • Hesse, C.H.1
  • 20
    • 0011629004 scopus 로고    scopus 로고
    • Data-driven deconvolution
    • Hesse, C. H. (1999) Data-driven deconvolution. J. Nonparam. Statist., 10, 343-373.
    • (1999) J. Nonparam. Statist. , vol.10 , pp. 343-373
    • Hesse, C.H.1
  • 21
    • 0033571404 scopus 로고    scopus 로고
    • Regression with covariates and outcome calculated from a common set of variables measured with error: Estimation using the SIMEX method
    • Holcomb, J. P. (1999) Regression with covariates and outcome calculated from a common set of variables measured with error: estimation using the SIMEX method. Statist. Med., 18, 2847-2862.
    • (1999) Statist. Med. , vol.18 , pp. 2847-2862
    • Holcomb, J.P.1
  • 22
    • 0040579768 scopus 로고    scopus 로고
    • Isotonic inverse estimators for nonparametric deconvolution
    • Jongbloed, G. and van Zuijlen, M. (1998) Isotonic inverse estimators for nonparametric deconvolution. Ann. Statist., 26, 2395-2406.
    • (1998) Ann. Statist. , vol.26 , pp. 2395-2406
    • Jongbloed, G.1    Van Zuijlen, M.2
  • 23
    • 1042274766 scopus 로고    scopus 로고
    • SIMEX approaches to measurement error in ROC studies
    • Kim, J. and Gleser, L. J. (2000) SIMEX approaches to measurement error in ROC studies. Communs Statist. Theory Meth., 29, 2473-2491.
    • (2000) Communs Statist. Theory Meth. , vol.29 , pp. 2473-2491
    • Kim, J.1    Gleser, L.J.2
  • 24
    • 0033045888 scopus 로고    scopus 로고
    • SIMEX variance component tests in generalized linear mixed measurement error models
    • Lin, X. H. and Carroll, R. J. (1999) SIMEX variance component tests in generalized linear mixed measurement error models. Biometrics, 55, 613-619.
    • (1999) Biometrics , vol.55 , pp. 613-619
    • Lin, X.H.1    Carroll, R.J.2
  • 25
    • 1542427460 scopus 로고    scopus 로고
    • Nonparametric function estimation for clustered data when the predictor is measured without/with error
    • Lin, X. H. and Carroll, R. J. (2000) Nonparametric function estimation for clustered data when the predictor is measured without/with error. J. Am. Statist. Ass., 95, 520-534.
    • (2000) J. Am. Statist. Ass. , vol.95 , pp. 520-534
    • Lin, X.H.1    Carroll, R.J.2
  • 26
    • 84988058829 scopus 로고
    • A consistent nonparametric density estimator for the deconvolution problem
    • Liu, M. C. and Taylor, R. (1989) A consistent nonparametric density estimator for the deconvolution problem. Can. J. Statist., 17, 427-438.
    • (1989) Can. J. Statist. , vol.17 , pp. 427-438
    • Liu, M.C.1    Taylor, R.2
  • 27
    • 0006944268 scopus 로고    scopus 로고
    • Estimation of the CDF of a finite population in the presence of a calibration sample
    • Luo, M., Stokes, L. and Sager, T. (1998) Estimation of the CDF of a finite population in the presence of a calibration sample. Environ. Ecol. Statist., 5, 277-289.
    • (1998) Environ. Ecol. Statist. , vol.5 , pp. 277-289
    • Luo, M.1    Stokes, L.2    Sager, T.3
  • 28
    • 0002454664 scopus 로고
    • Strong consistency and rates for deconvolution of multivariate densities of stationary processes
    • Masry, E. (1993) Strong consistency and rates for deconvolution of multivariate densities of stationary processes. Stoch. Processes Appl., 47, 53-74.
    • (1993) Stoch. Processes Appl. , vol.47 , pp. 53-74
    • Masry, E.1
  • 29
    • 0000556630 scopus 로고
    • Deconvolution of microfluorometric histograms with B splines
    • Mendelsohn, J. and Rice, J. A. (1982) Deconvolution of microfluorometric histograms with B splines. J. Am. Statist. Ass., 77, 748-753.
    • (1982) J. Am. Statist. Ass. , vol.77 , pp. 748-753
    • Mendelsohn, J.1    Rice, J.A.2
  • 30
    • 0035998836 scopus 로고    scopus 로고
    • Corrected score estimation via complex variable simulation extrapolation
    • Novick, S. J. and Stefanski, L. A. (2002) Corrected score estimation via complex variable simulation extrapolation. J. Am. Statist. Ass., 97, 472-481.
    • (2002) J. Am. Statist. Ass. , vol.97 , pp. 472-481
    • Novick, S.J.1    Stefanski, L.A.2
  • 31
    • 0033234633 scopus 로고    scopus 로고
    • Adaptive wavelet estimator for nonparametric density deconvolution
    • Pensky, M. and Vidakovic, B. (1999) Adaptive wavelet estimator for nonparametric density deconvolution. Ann. Statist., 27, 2033-2053.
    • (1999) Ann. Statist. , vol.27 , pp. 2033-2053
    • Pensky, M.1    Vidakovic, B.2
  • 32
    • 0010027636 scopus 로고    scopus 로고
    • Empirical-bias bandwidths for local polynomial nonparametric regression and density estimation
    • Ruppert, D. (1997) Empirical-bias bandwidths for local polynomial nonparametric regression and density estimation. J. Am. Statist. Ass., 92, 1049-1062.
    • (1997) J. Am. Statist. Ass. , vol.92 , pp. 1049-1062
    • Ruppert, D.1
  • 33
    • 1042290928 scopus 로고    scopus 로고
    • Local polynomial regression and simulation-extrapolation
    • Staudenmeyer, J. and Ruppert, D. (2004) Local polynomial regression and simulation-extrapolation. J. R. Statist. Soc. B, 66, 17-30.
    • (2004) J. R. Statist. Soc. B , vol.66 , pp. 17-30
    • Staudenmeyer, J.1    Ruppert, D.2
  • 34
    • 38249019182 scopus 로고
    • Rates of convergence of some estimators in a class of deconvolution problems
    • Stefanski, L. (1990) Rates of convergence of some estimators in a class of deconvolution problems. Statist. Probab. Lett., 9, 229-235.
    • (1990) Statist. Probab. Lett. , vol.9 , pp. 229-235
    • Stefanski, L.1
  • 35
    • 0442309427 scopus 로고    scopus 로고
    • Measurement error models
    • Stefanski, L. (2000) Measurement error models. J. Am. Statist. Ass., 95, 1353-1358.
    • (2000) J. Am. Statist. Ass. , vol.95 , pp. 1353-1358
    • Stefanski, L.1
  • 36
    • 0007476791 scopus 로고    scopus 로고
    • Simulation extrapolation deconvolution of finite population cumulative distribution function estimators
    • Stefanski, L. A. and Bay, J. M. (1996) Simulation extrapolation deconvolution of finite population cumulative distribution function estimators. Biometrika, 83, 407-417.
    • (1996) Biometrika , vol.83 , pp. 407-417
    • Stefanski, L.A.1    Bay, J.M.2
  • 37
    • 84972949113 scopus 로고
    • Deconvolving kernel density estimators
    • Stefanski, L. and Carroll, R. J. (1990) Deconvolving kernel density estimators. Statistics, 21, 169-184.
    • (1990) Statistics , vol.21 , pp. 169-184
    • Stefanski, L.1    Carroll, R.J.2
  • 38
    • 84950433368 scopus 로고
    • Simulation-extrapolation: The measurement error jackknife
    • Stefanski, L. A. and Cook, R. J. (1995) Simulation-extrapolation: the measurement error jackknife. J. Am. Statist. Ass., 90, 1247-1256.
    • (1995) J. Am. Statist. Ass. , vol.90 , pp. 1247-1256
    • Stefanski, L.A.1    Cook, R.J.2
  • 39
    • 0034522905 scopus 로고    scopus 로고
    • Measurement error correction using validation data: A review of methods and their applicability in case-control studies
    • Thurigen, D., Spiegelman, D., Blettner, M., Heurer, C. and Brenner, H. (2000) Measurement error correction using validation data: a review of methods and their applicability in case-control studies. Statist. Meth. Med Res., 9, 447-474.
    • (2000) Statist. Meth. Med Res. , vol.9 , pp. 447-474
    • Thurigen, D.1    Spiegelman, D.2    Blettner, M.3    Heurer, C.4    Brenner, H.5
  • 40
    • 0032519224 scopus 로고    scopus 로고
    • Finite sample performance of deconvolving kernel density estimators
    • Wand, M. P. (1998) Finite sample performance of deconvolving kernel density estimators. Statist. Probab. Lett., 37, 131-139.
    • (1998) Statist. Probab. Lett. , vol.37 , pp. 131-139
    • Wand, M.P.1
  • 41
    • 0029885621 scopus 로고    scopus 로고
    • Quasilikelihood estimation in measurement error models with correlated replicates
    • Wang, N., Carroll, R. J. and Liang, K. Y. (1996) Quasilikelihood estimation in measurement error models with correlated replicates. Biometrics, 52, 401-411.
    • (1996) Biometrics , vol.52 , pp. 401-411
    • Wang, N.1    Carroll, R.J.2    Liang, K.Y.3
  • 42
    • 0033442314 scopus 로고    scopus 로고
    • Change-points via wavelets for indirect data
    • Wang, Y. Z. (1999) Change-points via wavelets for indirect data. Statist. Sin., 9, 103-117.
    • (1999) Statist. Sin. , vol.9 , pp. 103-117
    • Wang, Y.Z.1
  • 43
    • 0038392287 scopus 로고    scopus 로고
    • Least squares cross-validation for the kernel deconvolution density estimator
    • Youndje, T. and Wells, M. T. (2002) Least squares cross-validation for the kernel deconvolution density estimator. C. R. Math. Acad. Sci., 334, 509-513.
    • (2002) C. R. Math. Acad. Sci. , vol.334 , pp. 509-513
    • Youndje, T.1    Wells, M.T.2
  • 44
    • 0036568428 scopus 로고    scopus 로고
    • Deconvolving multidimensional density from partially contaminated observations
    • Yuan, M. and Chen, J. Q. (2002) Deconvolving multidimensional density from partially contaminated observations. J. Statist. Planng Inf., 104, 147-160.
    • (2002) J. Statist. Planng Inf. , vol.104 , pp. 147-160
    • Yuan, M.1    Chen, J.Q.2
  • 45
    • 0002055609 scopus 로고
    • Fourier methods for estimating mixing densities and distributions
    • Zhang, C.-H. (1990) Fourier methods for estimating mixing densities and distributions. Ann. Statist., 18, 806-831.
    • (1990) Ann. Statist. , vol.18 , pp. 806-831
    • Zhang, C.-H.1
  • 46
    • 6744242017 scopus 로고    scopus 로고
    • Boundary bias correction for nonparametric deconvolution
    • Zhang, S. P. and Karunamuni, R. J. (2000) Boundary bias correction for nonparametric deconvolution. Ann. Inst. Statist. Math., 52, 612-629.
    • (2000) Ann. Inst. Statist. Math. , vol.52 , pp. 612-629
    • Zhang, S.P.1    Karunamuni, R.J.2


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