Large-sample inference for the general half-normal distribution

Communications in Statistics - Theory and Methods

Volumn 31, Issue 7, 2002, Pages 1045-1054

  Pewsey, Arthur ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

Confidence sets; General half normal distribution; Large sample inference; Maximum likelihood estimation; Non regular problem

Indexed keywords

EID: 31244438282     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1081/STA-120004901     Document Type: Article

References (22)

1. Johnson, N.L.; Kotz, S.; Balakrishnan, N. Continuous Univariate Distributions, Vol. 1, 2nd Ed.; Wiley: New York, 1994.
2. Azzalini, A. A Class of Distributions Which Includes the Normal Ones. Scandinavian Journal of Statistics 1985, 12, 171-178.
3. Azzalini, A.; Capitanio, A. Statistical Applications of the Multivariate Skew-normal Distribution. Journal of the Royal Statistical Society, Series B 1999, 61, 579-602.
4. Pewsey, A. Problems of Inference for Azzalini's Skew-Normal Distribution. Journal of Applied Statistics 2000, 27, 859-870.
5. Daniel, C. Use of Half Normal Plots in Interpreting Factorial Two-Level Experiments. Technometrics 1959, 1, 311-341.
6. Aigner, D.J.; Lovell, C.A.K.; Schmidt, P. J. Formulation and Estimation of Stochastic Frontier Production Function Models. Journal of Econometrics 1977, 6, 21-37.
7. Polfeldt, T. Asymptotic Results in Non-Regular Estimation. Scandinavian Actuarial Journal 1970, 1-2 Supplement.
8. Cheng, R.C.H.; Traylor, L. Non-regular Maximum Likelihood Problems. Journal of the Royal Statistical Society, Series B 1995, 61, 3-44.
9. Smith, R.L. Maximum Likelihood Estimation in a Class of Non-Regular Cases. Biometrika 1985, 72, 67-92.
10. Smith, R.L. A Survey of Nonregular Problems. In Proceedings of the International Statistical Institute Conference, 47th Session, Paris, 1989; 353-372.
11. Smith, R.L.; Naylor, J.C. A Comparison of Maximum Likelihood and Bayesian Estimators for the Three-Parameter Weibull Distribution. Applied Statistics 1987, 36, 358-369.
12. Cook, R.D.; Weisberg, S. An Introduction to Regression Graphics; Wiley: New York, 1994.
13. Mood, A.M. Introduction to the Theory of Statistics; McGraw-Hill: New York, 1950.
14. Arnold, B.C.; Shavelle, R.M. Joint Confidence Sets for the Mean and Variance of a Normal Distribution. The American Statistician 1998, 52, 133-140.
15. Wichman, B.A.; Hill, I.D. Algorithm AS 183: An Efficient and Portable Pseudo-Random Number Generator. Applied Statistics 1982, 31, 188-190.
16. McLeod, A.I. A Remark on AS183. An Efficient and Portable Pseudo-Random Number Generator. Applied Statistics 1985, 34, 198-200.
17. Henze, N. A Probabilistic Representation of the 'Skew-Normal' Distribution. Scandinavian Journal of Statistics 1986, 13, 271-275.
18. Neyman, J. Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability. Philosophical Transactions of the Royal Society 1937, 236, 333-380.
19. Lehmann, E.L. Testing Statistical Hypotheses; Wiley: New York, 1959; 78-83.
20. Atchison, J. Confidence-Region Tests. Journal of the Royal Statistical Society, Series B 1964, 26, 462-476.
21. Atchison, J. Likelihood-Ratio and Confidence-Region Tests. Journal of the Royal Statistical Society, Series B 1965, 27, 245-250.
22. Wilmore, J.H.; Costill, D.L. Physiology of Sport and Exercise; Human Kinetics: Champaign, Illinois, 1994.