Probability distributions and orthogonal parameters

V. S. Huzurbazar

doi:10.1017/S0305004100025743

Extract

Let f(x, αi) be the probability density function of a distribution depending on n parameters αi(i = 1,2, …, n). Then following Jeffreys(1) we shall say that the parameters αi are orthogonal if

References

REFERENCES

(1)Jeffreys, H.Theory of probability, 2nd ed. (Oxford, 1948), pp. 158, 184.Google Scholar

(2)Jeffreys, H.Phil. Trans. A, 237 (1938), 231–71.Google Scholar

(3)Eisenhart, L. P.Riemannian geometry (Princeton 1926), p. 43.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Mitchell, Ann F. S. 1962. Sufficient Statistics and Orthogonal Parameters. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 58, Issue. 2, p. 326.

Cox, D. R. and Reid, N. 1987. Parameter Orthogonality and Approximate Conditional Inference. Journal of the Royal Statistical Society Series B: Statistical Methodology, Vol. 49, Issue. 1, p. 1.

Hürlimann, W. 1992. On parameter orthogonality to the mean. Statistical Papers, Vol. 33, Issue. 1, p. 69.

Nicolaou, Anna 1993. Bayesian Intervals with Good Frequentist Behaviour in the Presence of Nuisance Parameters. Journal of the Royal Statistical Society Series B: Statistical Methodology, Vol. 55, Issue. 2, p. 377.

Gupta, A. K. and Székely, G. J. 1994. On location and scale maximum likelihood estimators. Proceedings of the American Mathematical Society, Vol. 120, Issue. 2, p. 585.

Laskar, Mizan R. and King, Maxwell L. 1998. Estimation and testing of regression disturbances based on modified likelihood functions. Journal of Statistical Planning and Inference, Vol. 71, Issue. 1-2, p. 75.

Um, Jongseok 2003. Inference about Measure of Agreement in the General Mixture Model via Parameter Orthogonalization. Communications for Statistical Applications and Methods, Vol. 10, Issue. 2, p. 341.

Reid, Nancy 2005. Encyclopedia of Statistical Sciences.

Basseville, M. and Nikiforov, I. 2005. Handling nuisance parameters in systems monitoring. p. 3832.

He, Heping and Severini, Thomas A. 2007. Higher-order asymptotic normality of approximations to the modified signed likelihood ratio statistic for regular models. The Annals of Statistics, Vol. 35, Issue. 5,

Ghosh, M. Mukherjee, B. Santra, U. and Kim, D. 2010. Bayesian and likelihood-based inference for the bivariate normal correlation coefficient. Journal of Statistical Planning and Inference, Vol. 140, Issue. 6, p. 1410.

Ghosh, Malay 2011. Objective Priors: An Introduction for Frequentists. Statistical Science, Vol. 26, Issue. 2,

Bakhshi, Andisheh Senn, Stephen and Phillips, Alan 2013. Some issues in predicting patient recruitment in multi‐centre clinical trials. Statistics in Medicine, Vol. 32, Issue. 30, p. 5458.

2014. Information and Exponential Families. p. 221.

Reid, Nancy 2014. Wiley StatsRef: Statistics Reference Online.

Heller, Gillian Z. Couturier, Dominique‐Laurent and Heritier, Stephane R. 2019. Beyond mean modelling: Bias due to misspecification of dispersion in Poisson‐inverse Gaussian regression. Biometrical Journal, Vol. 61, Issue. 2, p. 333.

Niemczyk, Marcela and Iskander, D. Robert 2021. Statistical analysis of corneal OCT speckle: a non-parametric approach. Biomedical Optics Express, Vol. 12, Issue. 10, p. 6407.

Selig, Katharina Shaw, Pamela and Ankerst, Donna 2021. Bayesian information criterion approximations to Bayes factors for univariate and multivariate logistic regression models. The International Journal of Biostatistics, Vol. 17, Issue. 2, p. 241.

Moins, Théo Arbel, Julyan Girard, Stéphane and Dutfoy, Anne 2023. Reparameterization of extreme value framework for improved Bayesian workflow. Computational Statistics & Data Analysis, Vol. 187, Issue. , p. 107807.

Nascimento, Abraão D.C. Vasconcelos, Josimar M. Cintra, Renato J. and Frery, Alejandro C. 2024. Regression model for speckled data with extreme variability. ISPRS Journal of Photogrammetry and Remote Sensing, Vol. 213, Issue. , p. 1.

Article contents

Probability distributions and orthogonal parameters

Extract

Access options

References

REFERENCES

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Probability distributions and orthogonal parameters

Extract

Access options

References

REFERENCES

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests