Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-30T15:06:52.512Z Has data issue: false hasContentIssue false
  • English
  • Français

REGRESSION DEPENDENCE IN LATENT VARIABLE MODELS

Published online by Cambridge University Press:  06 March 2006

Taizhong Hu ,
Jing Chen  and
Chaode Xie
Taizhong Hu
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China, E-mail: [email protected]
Jing Chen
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China, E-mail: [email protected]
Chaode Xie
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Three new notions of positive dependence (positive regression dependence, positive left-tail regression dependence, and positive right-tail regression dependence) are studied in this article. Consider a latent variable model where the manifest random variables T1,T2,…,Tn given latent random variable/vector (Θ1,…,Θm) are conditional independent. Conditions are identified under which T1,…,Tn possesses the new dependence notions for different types of latent variable model. Applications of the results are also provided.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 2 , April 2006 , pp. 363 - 379
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart & Winston.
Belzunce, F., Lillo, R.E., Pellerey, F., & Shaked, M. (2002). Preservation of association in multivariate shock and claim models. Operation Research Letters 30: 223–230.Google Scholar
Belzunce, F. & Semeraro, P. (2004). Preservation of positive (negative) orthant dependence concepts under mixtures and applications. Journal of Applied Probability 41: 961–974.Google Scholar
Blessinger, T. (2002). More on stochastic comparisons and dependence among concomitants of order statistics. Journal of Multivariate Analysis 82: 367–378.Google Scholar
Block, H.W. & Ting, M. (1981). Some concepts of multivariate dependence. Communications in Statistics: Theory and Methods 10: 749–762.Google Scholar
Colangelo, A., Scarsini, M., & Shaked, M. (2005). Some notions of multivariate positive dependence. Insurance: Mathematics and Economics 37: 13–26.Google Scholar
David, H.A. & Nagaraja, H.N. (1998). Concomitants of order statistics. In N. Balakrishnan & C.R. Rao (eds.), Handbook of statistics, Vol. 16: Order statistics: Theory and methods. New York: Elsevier. pp. 487–513.
Dubhashi, D. & Ranjan, D. (1998). Balls and bins: A study in negative dependence. Random Structures Algorithms 13: 99–124.Google Scholar
Esary, J.D., Proschan, F., & Walkup, D.W. (1967). Association of random variables with applications. Annals of Mathematical Statistics 44: 1466–1474.Google Scholar
Harris, R. (1970). A multivariate definition for increasing hazard rate distribution functions. Annals of Mathematical Statistics 41: 713–717.Google Scholar
Holland, P.W. & Rosenbaum, P.R. (1986). Conditional association and unidimensionality in monotone latent variable models. Annals of Statistics 14: 1523–1543.Google Scholar
Hu, T. & Xie, C. (2006). Negative dependence in the balls and bins experiment with applications to order statistics. Journal of Multivariate Analysis (in press).CrossRef
Jogdeo, K. (1978). On a probability bound of Marshall and Olkin. Annals of Statistics 6: 232–234.Google Scholar
Karlin, S. & Rinott, Y. (1980). Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions. Journal of Multivariate Analysis 10: 467–498.Google Scholar
Khaledi, B.-E. & Kochar, S.C. (2000). Stochastic comparisons and dependence among concomitants of order statistics. Journal of Multivariate Analysis 73: 261–281.Google Scholar
Khaledi, B.-E. & Kochar, S.C. (2001). Dependence properties of multivariate mixture distributions and their applications. Annals of the Institute of Statistical Mathematics 53: 620–630.Google Scholar
Lee, M.-L.T. (1985). Dependence by total positivity. Annals of Probability 13: 572–582.Google Scholar
Lindqvist, B.H. (1988). Association of probability measures on partially ordered spaces. Journal of Multivariate Analysis 26: 111–132.Google Scholar
Müller, A. & Scarsini, M. (2001). Stochastic comparison of random vectors with a common copula. Mathematics of Operations Research 26: 723–740.Google Scholar
Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. West Sussex, UK: Wiley.
Norros, I. (1985). Systems weakened by failure. Stochastic Processes and Their Applications 20: 181–196.Google Scholar
Scarsini, M. & Spizzichino, F. (1999). Simpson-type paradoxes, dependence and ageing. Journal of Applied Probability 36: 119–131.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1990). Multivariate stochastic orderings and positive dependence in reliability theory. Mathematics of Operations Research 15: 545–552.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. New York: Academic Press.
Shaked, M. & Spizzichino, F. (1998). Positive dependence properties of conditionally independent random lifetimes. Mathematics of Operations Research 23: 944–959.Google Scholar
Tong, Y.L. (1989). Inequalities for a class of positively dependent random variables with a common marginal. The Annals of Statistics 17: 429–435.Google Scholar
Tong, Y.L. (1990). The multivariate normal distribution. New York: Springer-Verlag.CrossRef