Logistic regression with homoscedastic errors--A Berkson model

Author:
S. V. Shklyar

Translated by:
N. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **85** (2011).

Journal:
Theor. Probability and Math. Statist. **85** (2012), 169-180

MSC (2010):
Primary 62J12; Secondary 62G20

Published electronically:
January 14, 2013

MathSciNet review:
2933712

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Abstract | References | Similar Articles | Additional Information

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.

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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

DOI:
https://doi.org/10.1090/S0094-9000-2013-00883-7

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