- Volume 23 Issue 4
In this paper, two new inverse regression methods are introduced. One is a distance based method, and the other is a likelihood based method. While a model is fitted by minimizing the sum of squared prediction errors of y's and x's in the classical and inverse methods, respectively. In the new distance based method, we simultaneously minimize the sum of both squared prediction errors. In the likelihood based method, we propose an inverse regression with Arnold-Beaver Skew Normal(ABSN) error distribution. Using the cross validation method with an asymmetric real data set, two new and two existing methods are studied based on the relative prediction bias(RBP) criteria.
Arnold-Beaver skew normal distribution;asymmetric data;inverse regression;calibration;relative prediction bias
- Arnold, B. and Beaver, R. (2000). Hidden truncation models, Sankhya, 62, 23–35.
- Brown, G. H. (1979). An optimization criterion for linear inverse estimation, Technometrics, 21, 727–736.
- Chow, S. and Shao, J. (1990). On the difference between the classical and inverse methods of calibration, Applied Statistics, 39, 219–228. https://doi.org/10.2307/2347761
- Halperin, M. (1970). On inverse estimation in linear regression, Technometrics, 12, 595–601.
- Kim, S. (2009). Inverse Circular Regression with Possibly Asymmetric Error Distribution, PhD Dissertation, University of California, Riverside.
- Krutchkoff, R. G. (1967). Classical and inverse regression methods of calibration, Technometrics, 9, 425–439. https://doi.org/10.2307/1266511
- Krutchkoff, R. G. (1969). Classical and inverse regression methods of calibration in extrapolation (in notes), Technometrics, 11, 605–608.
- Martinelle, S. (1970). On the choice of regression in linear calibration, Technometrics, 12, 157–161. https://doi.org/10.2307/1267361
- Minder, C. E. and Whitney, J. B. (1975). A likelihood analysis of the linear calibration problem, Technometrics, 17, 463–471. https://doi.org/10.2307/1268433
- Pitman, E. (1937). The closest estimates of statistical parameters, Proceedings of the Cambridge Philosophical Society, 33, 212–222. https://doi.org/10.1017/S0305004100019563