scholarly journals Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations

2004 ◽  
Vol 32 (3) ◽  
pp. 1796-1829 ◽  
Author(s):  
Giovanni Peccati
Keyword(s):  
Symmetric Statistics

A Poisson limit theorem for incomplete symmetric statistics

1983 ◽  
Vol 20 (01) ◽  
pp. 47-60 ◽  
Author(s):  
M. Berman ◽  
G. K. Eagleson
Keyword(s):  
Limit Theorem ◽  
Limit Theorems ◽  
Random Variables ◽  
Asymptotic Distributions ◽  
Poisson Limit ◽  
Symmetric Statistics ◽  
Limit Result ◽  
Independent Identically Distributed

Silverman and Brown (1978) have derived Poisson limit theorems for certain sequences of symmetric statistics, based on a sample of independent identically distributed random variables. In this paper an incomplete version of these statistics is considered and a Poisson limit result shown to hold. The powers of some tests based on the incomplete statistic are investigated and the main results of the paper are used to simplify the derivations of the asymptotic distributions of some statistics previously published in the literature.

Symmetric Statistics

1990 ◽  
pp. 69-88
Author(s):  
Rabi Bhattacharya ◽  
Manfred Denker
Keyword(s):  
Symmetric Statistics

scholarly journals What Makes an Annular Mode “Annular”?

2017 ◽  
Vol 74 (2) ◽  
pp. 317-332 ◽  
Author(s):  
Edwin P. Gerber ◽  
David W. J. Thompson
Keyword(s):  
Numerical Models ◽  
Atmospheric Model ◽  
External Forcing ◽  
Eof Analysis ◽  
Mean Flow ◽  
Orthogonal Function ◽  
The Mean ◽  
High Degree ◽  
Symmetric Statistics ◽  
Variance Explained

Abstract Annular patterns with a high degree of zonal symmetry play a prominent role in the natural variability of the atmospheric circulation and its response to external forcing. But despite their apparent importance for understanding climate variability, the processes that give rise to their marked zonally symmetric components remain largely unclear. Here the authors use simple stochastic models in conjunction with an atmospheric model and observational analyses to explore the conditions under which annular patterns arise from empirical orthogonal function (EOF) analysis of the flow. The results indicate that annular patterns arise not only from zonally coherent fluctuations in the circulation (i.e., “dynamical annularity”) but also from zonally symmetric statistics of the circulation in the absence of zonally coherent fluctuations (i.e., “statistical annularity”). It is argued that the distinction between dynamical and statistical annular patterns derived from EOF analysis can be inferred from the associated variance spectrum: larger differences in the variance explained by an annular EOF and successive EOFs generally indicate underlying dynamical annularity. The authors provide a simple recipe for assessing the conditions that give rise to annular EOFs of the circulation. When applied to numerical models, the recipe indicates dynamical annularity in parameter regimes with strong feedbacks between eddies and the mean flow. When applied to observations, the recipe indicates that annular EOFs generally derive from statistical annularity of the flow in the midlatitude troposphere but from dynamical annularity in both the stratosphere and the mid–high-latitude Southern Hemisphere troposphere.

A Useful Property of Some Symmetric Statistics

1984 ◽  
Vol 38 (1) ◽  
pp. 63 ◽  
Author(s):  
Timothy C. Brown ◽  
Geoffrey K. Eagleson
Keyword(s):  
Symmetric Statistics

scholarly journals Asymptotic Distribution of Symmetric Statistics

1980 ◽  
Vol 8 (1) ◽  
pp. 165-170 ◽  
Author(s):  
H. Rubin ◽  
R. A. Vitale
Keyword(s):  
Asymptotic Distribution ◽  
Symmetric Statistics

scholarly journals Empirical Edgeworth expansions for symmetric statistics

1998 ◽  
Vol 26 (4) ◽  
pp. 1540-1569 ◽  
Author(s):  
Hein Putter ◽  
Willem R. van Zwet
Keyword(s):  
Edgeworth Expansions ◽  
Symmetric Statistics
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