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Third-order likelihood-based inference for the log-normal regression model

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  • Chwu-Shiun Tarng

Abstract

This paper examines the general third-order theory to the log-normal regression model. The interest parameter is its conditional mean. For inference, traditional first-order approximations need large sample sizes and normal-like distributions. Some specific third-order methods need the explicit forms of the nuisance parameter and ancillary statistic, which are quite complicated. Note that this general third-order theory can be applied to any continuous models with standard asymptotic properties. It only needs the log-likelihood function. With small sample settings, the simulation studies for confidence intervals of the conditional mean illustrate that the general third-order theory is much superior to the traditional first-order methods.

Suggested Citation

  • Chwu-Shiun Tarng, 2014. "Third-order likelihood-based inference for the log-normal regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1976-1988, September.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:9:p:1976-1988
    DOI: 10.1080/02664763.2014.898134
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    References listed on IDEAS

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    1. Rekkas, M. & Wong, A., 2005. "Third-order inference for the Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 499-525, April.
    2. Fraser, D.A.S. & Rekkas, M. & Wong, A., 2005. "Highly accurate likelihood analysis for the seemingly unrelated regression problem," Journal of Econometrics, Elsevier, vol. 127(1), pages 17-33, July.
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