Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions
A function f(x) defined on = 1 - 2 - ... - n where each i is totally ordered satisfying f(x [logical or] y) f(x [logical and] y) >= f(x) f(y), where the lattice operations [logical or] and [logical and] refer to the usual ordering on , is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,..., Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix [Sigma] satisfies -D[Sigma]-1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 10 (1980)
Issue (Month): 4 (December)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:10:y:1980:i:4:p:467-498. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.