A corrected $T(q)$-likelihood estimator for the exponential structural measurement error model
Author:
A. V. Savchenko
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 86 (2013), 193-203
MSC (2010):
Primary 62J12
DOI:
https://doi.org/10.1090/S0094-9000-2013-00898-9
Published electronically:
August 20, 2013
MathSciNet review:
2986459
Full-text PDF Free Access
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Additional Information
Abstract: The exponential structural measurement error regression model is studied. The corrected $T(q)$-likelihood estimator of regression coefficients is constructed. A sufficient condition for the strong consistency of the estimator is presented for the case where the sample size tends to infinity, $q$ depends on the sample size, and $q\to 1$.
References
- Chi-Lun Cheng and Hans Schneeweiss, Polynomial regression with errors in the variables, J. R. Stat. Soc. Ser. B Stat. Methodol. 60 (1998), no. 1, 189–199. MR 1625632, DOI https://doi.org/10.1111/1467-9868.00118
- Davide Ferrari and Yuhong Yang, Maximum ${\rm L}q$-likelihood estimation, Ann. Statist. 38 (2010), no. 2, 753–783. MR 2604695, DOI https://doi.org/10.1214/09-AOS687
- N. Kolev, Maximum $T(q)$-Likelihood Estimation: a New Method and its Application in Risk Management, $6^{th}$ Conference in Actuarial Science & Finance on Samos, 2010, p. 22.
- A. Kukush and H. Schneeweiss, Comparing different estimators in a nonlinear measurement error model. I, Math. Methods Statist. 14 (2005), no. 1, 53–79. MR 2158071
- A. Kukush, I. Markovsky, and S. Van Huffel, Consistent estimation in the bilinear multivariate errors-in-variables model, Metrika 57 (2003), no. 3, 253–285. MR 1986189, DOI https://doi.org/10.1007/s001840200217
- O. S. Usol′tseva, A consistent estimator in the accelerated failure time model with censored observations and measurement errors, Teor. Ĭmovīr. Mat. Stat. 82 (2010), 156–162 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 82 (2011), 161–169. MR 2790491, DOI https://doi.org/10.1090/S0094-9000-2011-00835-6
References
- C.-L. Cheng and H. Schneeweiss, Polynomial regression with errors in the variables, J. R. Stat. Society B 60 (1998), 189–199. MR 1625632
- D. Ferrari and Y. Yang, Maximum $Lq$-likelihood estimation, Ann. Statist. 38 (2010), 753–783. MR 2604695 (2011c:62069)
- N. Kolev, Maximum $T(q)$-Likelihood Estimation: a New Method and its Application in Risk Management, $6^{th}$ Conference in Actuarial Science & Finance on Samos, 2010, p. 22.
- A. Kukush and H. Schneeweiss, Comparing different estimators in a non-linear measurement error model, I. Math. Methods Statist. 14 (2005), 53–79. MR 2158071 (2006j:62068a)
- A. Kukush,I. Markovsky, and S. Van Huffel, Consistent adjusted least squares estimator for errors-in-variables model $AXB=C$, Metrika 57 (2003), 253–285. MR 1986189 (2004d:62098)
- O. S. Usol’tseva, A consistent estimator in the accelerated failure time model with censored observations and measurement errors, Teor. Imovir. Matem. Statyst. 82 (2010), 156–162; English transl. in Theory Probab. Math. Stat. 82 (2011), 161–169. MR 2790491 (2011m:62346)
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Additional Information
A. V. Savchenko
Affiliation:
Department of Mathematical Analysis, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine
Email:
nebulous@bigmir.net
Keywords:
Exponential structural model,
measurement error,
$T(q)$-likelihood estimator,
corrected estimation function
Received by editor(s):
June 2, 2011
Published electronically:
August 20, 2013
Article copyright:
© Copyright 2013
American Mathematical Society
