Matches in SemOpenAlex for { <https://semopenalex.org/work/W2033996695> ?p ?o ?g. }
Showing items 1 to 60 of
60
with 100 items per page.
- W2033996695 endingPage "270" @default.
- W2033996695 startingPage "253" @default.
- W2033996695 abstract "The empirical mean of n independent and identically distributed (i.i.d.) random variables ((X_1,dots ,X_n)) can be viewed as a suitably normalized scalar projection of the n-dimensional random vector (X^{(n)}displaystyle mathop {=}^{cdot },(X_1,dots ,X_n)) in the direction of the unit vector (n^{-1/2}(1,1,dots ,1) in mathbb {S}^{n-1}). The large deviation principle (LDP) for such projections as (nrightarrow infty ) is given by the classical Cramer’s theorem. We prove an LDP for the sequence of normalized scalar projections of (X^{(n)}) in the direction of a generic unit vector (theta ^{(n)}in mathbb {S}^{n-1}), as (nrightarrow infty ). This LDP holds under fairly general conditions on the distribution of (X_1), and for “almost every” sequence of directions ((theta ^{(n)})_{nin mathbb {N}}). The associated rate function is “universal” in the sense that it does not depend on the particular sequence of directions. Moreover, under mild additional conditions on the law of (X_1), we show that the universal rate function differs from the Cramer rate function, thus showing that the sequence of directions (n^{-1/2}(1,1,dots ,1) in mathbb {S}^{n-1},) (n in mathbb {N}), corresponding to Cramer’s theorem is atypical." @default.
- W2033996695 created "2016-06-24" @default.
- W2033996695 creator A5021938540 @default.
- W2033996695 creator A5028049323 @default.
- W2033996695 creator A5072223676 @default.
- W2033996695 date "2016-01-01" @default.
- W2033996695 modified "2023-09-23" @default.
- W2033996695 title "Cramér’s Theorem is Atypical" @default.
- W2033996695 cites W1964171198 @default.
- W2033996695 cites W1976493872 @default.
- W2033996695 cites W1981301100 @default.
- W2033996695 cites W1992955670 @default.
- W2033996695 cites W2044915386 @default.
- W2033996695 cites W2047341691 @default.
- W2033996695 cites W2113166622 @default.
- W2033996695 cites W2143648696 @default.
- W2033996695 cites W4249667877 @default.
- W2033996695 cites W4255372713 @default.
- W2033996695 cites W4301258660 @default.
- W2033996695 cites W1511948180 @default.
- W2033996695 doi "https://doi.org/10.1007/978-3-319-34139-2_11" @default.
- W2033996695 hasPublicationYear "2016" @default.
- W2033996695 type Work @default.
- W2033996695 sameAs 2033996695 @default.
- W2033996695 citedByCount "12" @default.
- W2033996695 countsByYear W20339966952015 @default.
- W2033996695 countsByYear W20339966952016 @default.
- W2033996695 countsByYear W20339966952017 @default.
- W2033996695 countsByYear W20339966952018 @default.
- W2033996695 countsByYear W20339966952019 @default.
- W2033996695 countsByYear W20339966952020 @default.
- W2033996695 countsByYear W20339966952021 @default.
- W2033996695 countsByYear W20339966952022 @default.
- W2033996695 crossrefType "book-chapter" @default.
- W2033996695 hasAuthorship W2033996695A5021938540 @default.
- W2033996695 hasAuthorship W2033996695A5028049323 @default.
- W2033996695 hasAuthorship W2033996695A5072223676 @default.
- W2033996695 hasBestOaLocation W20339966952 @default.
- W2033996695 hasConcept C33923547 @default.
- W2033996695 hasConceptScore W2033996695C33923547 @default.
- W2033996695 hasLocation W20339966951 @default.
- W2033996695 hasLocation W20339966952 @default.
- W2033996695 hasOpenAccess W2033996695 @default.
- W2033996695 hasPrimaryLocation W20339966951 @default.
- W2033996695 hasRelatedWork W1974891317 @default.
- W2033996695 hasRelatedWork W2007596026 @default.
- W2033996695 hasRelatedWork W2044189972 @default.
- W2033996695 hasRelatedWork W2061531152 @default.
- W2033996695 hasRelatedWork W2069964982 @default.
- W2033996695 hasRelatedWork W2313400459 @default.
- W2033996695 hasRelatedWork W2911598644 @default.
- W2033996695 hasRelatedWork W2965437270 @default.
- W2033996695 hasRelatedWork W4225152035 @default.
- W2033996695 hasRelatedWork W4245490552 @default.
- W2033996695 isParatext "false" @default.
- W2033996695 isRetracted "false" @default.
- W2033996695 magId "2033996695" @default.
- W2033996695 workType "book-chapter" @default.