Matches in SemOpenAlex for { <https://semopenalex.org/work/W75953507> ?p ?o ?g. }
Showing items 1 to 43 of
43
with 100 items per page.
- W75953507 endingPage "577" @default.
- W75953507 startingPage "568" @default.
- W75953507 abstract "The laws of large numbers consist in that the empirical means converge to the theoretical ones. In the classical case, the arithmetic sample means under some conditions converge in probability, as the number of addends grow, to the mathematical expectation. The essence of the laws of large numbers is that they usually establish the consistency of a large body of statistical estimators. By and large, this topic seems to hold the lead in probability theory and mathematical statistics. Nevertheless, behind the mathematical apparatus used are properties of sums of random variables (or, generally speaking, elements of a linear space). Therefore, it cannot be applied to probabilistic problems related to objects of an arbitrary nature. These are binary relations, fuzzy sets, and, in general, the elements of spaces not endowed with a vector-like structure; they emerge rather frequently in applied studies (see [1–3]). In this connection, it seems pertinent to establish laws of large numbers in spaces of a nonnumerical nature. The following problems thus have to be solved. (A) To define the empirical mean. (B) To define the theoretical mean. (C) To introduce the convergence of the empirical means to the theoretical one. (D) To prove, under some conditions, the convergence of the empirical means to the theoretical one. (E) To justify the consistency of various statistical estimators. (F) To apply the results obtained to actual problems. The authors have been studying this topic since the 70s (see [4, 5]). But only recently have we succeeded in establishing the law of large numbers under quite natural constraints. This constitutes the dominant bulk of the present paper. In addition to generalizing [6], we give the results of computer analysis of the set of empirical means." @default.
- W75953507 created "2016-06-24" @default.
- W75953507 creator A5011163697 @default.
- W75953507 creator A5091041595 @default.
- W75953507 date "2001-01-01" @default.
- W75953507 modified "2023-09-24" @default.
- W75953507 cites W2077651660 @default.
- W75953507 cites W2802006459 @default.
- W75953507 cites W298607803 @default.
- W75953507 doi "https://doi.org/10.1023/a:1009502128796" @default.
- W75953507 hasPublicationYear "2001" @default.
- W75953507 type Work @default.
- W75953507 sameAs 75953507 @default.
- W75953507 citedByCount "0" @default.
- W75953507 crossrefType "journal-article" @default.
- W75953507 hasAuthorship W75953507A5011163697 @default.
- W75953507 hasAuthorship W75953507A5091041595 @default.
- W75953507 hasBestOaLocation W759535071 @default.
- W75953507 hasConcept C202444582 @default.
- W75953507 hasConcept C33923547 @default.
- W75953507 hasConceptScore W75953507C202444582 @default.
- W75953507 hasConceptScore W75953507C33923547 @default.
- W75953507 hasIssue "5" @default.
- W75953507 hasLocation W759535071 @default.
- W75953507 hasOpenAccess W75953507 @default.
- W75953507 hasPrimaryLocation W759535071 @default.
- W75953507 hasRelatedWork W1557945163 @default.
- W75953507 hasRelatedWork W1985218657 @default.
- W75953507 hasRelatedWork W2023661790 @default.
- W75953507 hasRelatedWork W2073994398 @default.
- W75953507 hasRelatedWork W2096753949 @default.
- W75953507 hasRelatedWork W2963341196 @default.
- W75953507 hasRelatedWork W3106133691 @default.
- W75953507 hasRelatedWork W3124205579 @default.
- W75953507 hasRelatedWork W3134646037 @default.
- W75953507 hasRelatedWork W4249580765 @default.
- W75953507 hasVolume "103" @default.
- W75953507 isParatext "false" @default.
- W75953507 isRetracted "false" @default.
- W75953507 magId "75953507" @default.
- W75953507 workType "article" @default.