Unbiased estimation of a nonlinear function a normal mean with application to measurement err oorf models

Bibliography

• Armstrong , B. 1985 . Measurement error in the generalized linear model . Comm. Statist , B14 : 529 – 44 .
   Google Scholar
• Bickel , P.J. and Ritov , Y. 1987 . Efficient estimation in the errors-in-variables model . Ann. Statist , 15 : 513 – 540 .
   Web of Science ®Google Scholar
• Carroll , R.J. , Spiegelman , C.H. , Lan , K.K. , Bailey , K.T. and Abbott , R.D. 1984 . On errors-in-variables for binary regression models . Biometrika , 71 : 19 – 25 .
   Web of Science ®Google Scholar
• Carroll , R.J. and Hall , P.J. 1988 . Optimal rates of convergence for deconvolving a density . J. Am. Statist. Assoc , 83 : 1184 – 1186 .
   Web of Science ®Google Scholar
• Cramér , H. “ On some classes of series used in mathematical statistics ” . In Sixth Scandinavian Congr. of Math , 399 Kobenhaven : Polish Scientific Publishers .
   Google Scholar
• Cramér , H. 1957 . “ Mathematical Methods of Statistics ” . Princeton : Princeton University Press .
   Google Scholar
• Ghosh , J.K. and Singh , R. 1966 . Unbiased estimation of location and scale parameters . Ann. Math. Statist , 37 : 1671 – 1675 .
   Google Scholar
• Huber , P.J. The behavior of maximum likelihood estimators under nonstandard conditions . Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics an Probability . Edited by: LeCam , L.M. and Neyman , J. Vol. 1 , pp. 221 – 233 . University of California Press .
   Google Scholar
• Liu M.C. Taylor R.L. A consistent nonparametric density estimator for the deconvolution problem University of Georgia, Department of Statistics 1987 Technical Report, STA 73
   Google Scholar
• Nakamura , T. 1989a . Corrected score function of errors-in- variables models: methodology and application to generalized linear model . Biometrika , 1 to appear
   Google Scholar
• Nakamura T. Inference of errors-in-variables models based on corrected likelihood 1989b Unpublished manuscript
   Google Scholar
• Neyman , J. and Scott , E.L. 1960 . Correction for bias induced by a transformation of variables . Ann. Math. Statist , 31 : 643 – 655 .
   Google Scholar
• Parzen , E. 1967 . “ Time Series Analysis Papers ” . San Francisco : Hoiden-Day .
   Google Scholar
• Schafer , D.W. 1987 . Covariate measurement error in generalized linear models . Biometrik , 74 : 385 – 391 .
   Web of Science ®Google Scholar
• Stefanski , L.A. 1985 . The effects of measurement error on parameter estimation . Biometrika , 72 : 583 – 592 .
   Web of Science ®Google Scholar
• Stefanski L.A. Unbiased estimation of a nonlinear function of a normal mean with application to measurement error models Cornell University Biometrics Unit 1985 Technical Report No. 85-28
   Google Scholar
• Stefanski , L.A. and Carroll , R.J. 1985 . Covariate measurement error in logistic regression . Ann. Statist , 13 : 1335 – 1351 .
   Web of Science ®Google Scholar
• Stefanski , L.A. and Carroll , R.J. 1989 . Deconvoluting kernel density estimators . Statistics , 13 to appear
   Google Scholar
• Stefanski , L.A. and Carroll , R.J. 1987 . Conditional scores and optimal scores for generalized linear measurement error models . Biometrika , 74 : 703 – 716 .
   Web of Science ®Google Scholar
• Stefanski , L.A. 1988 . Measurement errors in generalized linear model explanatory variables , Raleigh, NC : North Carolina State University . Institute of Statistics Mimeo Series No. 1926
   Google Scholar
• Stulajter , F. 1978 . Nonlinear estimators of polynomials in mean values of a Guassian stochastic process . Kybemetrika , 14 : 206 – 220 .
   Google Scholar
• Whittemore , A.S. and Keller , J.B. 1988 . Approximations for errors-in-variables regression . J.Am.Statist.Assoc , 83 : 1057 – 1066 .
   Web of Science ®Google Scholar
• Wolter , K.M. and Fuller , W.A. 1982 . Estimation of nonlinear errors-in-variables models . Ann. Statist , 10 : 539 – 548 .
   Web of Science ®Google Scholar