zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Ranking and selection from paired-comparison data (with discussion). (English) Zbl 0767.62021
The frontiers of modern statistical inference procedures, II, Proc. Discuss. 2nd Int. Conf., IPASRAS-II, Sydney/Aust. 1987, Am. Sci. Press Ser. Math. Manage. Sci. 28, 3-24 (1992).

Summary: [For the entire collection see Zbl 0759.00005.]

Subset selection and indifference zone approaches to the selection of the best object in a balanced paired-comparison experiment are reviewed. Weak and strong curtailment are introduced in this context. It is shown that the probability of correctly selecting the best object is the same under strong curtailment as for the completed experiment if the Bradley-Terry preference model holds.

For unbalanced paired-comparison data, with at most one comparison per pair, it is proposed to rank the objects on the basis of the following scoring system expressed in the language of tournaments: The score of a player A is the total number of (a) wins of players defeated by A minus losses of players to whom A lost, plus (b) A’s wins minus A’s losses. A tied match counts as half a win plus half a loss. More general experiments can be treated similarly.

MSC:
62F07Statistical ranking and selection procedures