Logistic regression with homoscedastic errors—A Berkson model
Author:
S. V. Shklyar
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 85 (2012), 169-180
MSC (2010):
Primary 62J12; Secondary 62G20
DOI:
https://doi.org/10.1090/S0094-9000-2013-00883-7
Published electronically:
January 14, 2013
MathSciNet review:
2933712
Full-text PDF Free Access
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Abstract: We consider a Berkson model of logistic regression with a single regressor and normally distributed homoscedastic errors in the regressor (the so-called Berkson model). The variance of the errors is assumed to be known. Sufficient conditions for the uniqueness of a solution of the limit estimating equation in the structural model, and sufficient conditions for the strong consistency of the maximum likelihood estimator are found in the paper.
References
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References
- T. W. Anderson, Introduction to Multivariate Statistical Analysis, Third edition, John Wiley & Sons, Hoboken, NJ, 2003. MR 1990662 (2004c:62001)
- D. Burr, On errors-in-variables in binary regression—Berkson case, J. Amer. Statist. Assoc. 83 (1988), no. 403, 739–743. MR 963801
- R. J. Carroll, D. Ruppert, L. A. Stefanski, and C. M. Crainiceanu, Measurement Error in Nonlinear Models: A Modern Perspective, Second edition, Chapman & Hall, London, 2006. MR 2243417 (2007e:62004)
- R. J. Carroll, C. H. Spiegelman, K. K. G. Lan, K. T. Bailey, and R. D. Abbott, On errors in variables in binary regression models, Biometrika 71 (1984), 19–26. MR 738321 (85e:62127)
- E. Crouch and D. Spiegelman, The evaluation of integrals of the form $\int _{-\infty }^\infty f(t) \exp (-t^2) dt$: application to logistic-normal models, J. Amer. Statist. Assoc. 85 (1990), no. 410, 464–469. MR 1141749 (92h:65032)
- M. V. Kartashov, Probability. Processes. Statistics, Kyiv University, Kyiv, 2008. (Ukrainian)
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- A. Kukush and H. Schneeweiss, Comparing different estimators in a nonlinear measurement error model. Part I, Math. Methods Statist. 14 (2005), 53–79. MR 2158071 (2006j:62068a)
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Additional Information
S. V. Shklyar
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email:
shklyar@mail.univ.kiev.ua
Keywords:
Logistic regression,
binary regression,
models with errors in variables,
Berkson model,
regression calibration model
Received by editor(s):
September 7, 2011
Published electronically:
January 14, 2013
Additional Notes:
The paper is based on the talk presented at the International Conference “Modern Stochastics: Theory and Applications II” held September 7–11, 2010, at Kyiv National Taras Shevchenko University and dedicated to the anniversaries of prominent Ukrainian scientists, Anatoliĭ Skorokhod, Vladimir Korolyuk, and Igor Kovalenko
Article copyright:
© Copyright 2013
American Mathematical Society
