SMALL SAMPLE INFERENCE IN LOCATION SCALE MODELS WITH STUDENT(λ) ERRORS

ABSTRACT

A third order accurate approximation to the p value in testing either the location or scale parameter in a location scale model with Student(λ) errors is introduced. The third order approximation is developed via an asymptotic method, based on exponential models and the saddlepoint approximation. Techniques are presented for the numerical computation of all quantities required for the third order approximation. To compare the accuracy of various asymptotic methods a numerical example and simulation study are included. The numerical example and simulation study illustrate that the third order method presented leads to a more accurate p value approximation compared to first order methods in Student(λ) models with small samples.

Keywords:

• Location scale models
• Likelihood asymptotics
• Saddlepoint approximation
• Student family

8. ACKNOWLEDGMENTS

Supported by the Statistical and Data Analysis Center, Harvard School of Public Health (grant 5 U01 A138855). I would like to thank an anonymous referee for invaluable comments that improved the manuscript greatly. I would also like to thank Dr. Jianrong Wu for his helpful comments.