zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A monotonicity property of the power function of multivariate tests. (English) Zbl 0970.62038
Summary: Let S= k=1 n X k X k ' , where the X k are independent observations from a 2-dimensional normal N(μ k ,Σ) distribution, and let Λ= k=1 n μ k μ k ' Σ -1 be a diagonal matrix of the form λI, where λ0 and I is the identity matrix. It is shown that the density φ of the vector ˜=( 1 , 2 ) of characteristic roots of S can be written as G(λ, 1 , 2 )φ 0 ( ˜), where G satisfies the FKG condition on + 3 . This implies that the power function of tests with monotone acceptance region in 1 and 2 , i.e. a region of the form {g( 1 , 2 )c}, where g is nondecreasing in each argument, is nondecreasing in λ. It is also shown that the density φ of ( 1 , 2 ) does not allow a decomposition φ( 1 , 2 )=G(λ, 1 , 2 )φ 0 ( ˜), with G satisfying the FKG condition, if Λ=diag(λ,0) and λ>0, implying that this approach to proving monotonicity of the power function fails in general.
62H15Multivariate hypothesis testing
62H10Multivariate distributions of statistics