scholarly journals RATE OF CONVERGENCE IN DISTRIBUTION OF A LINEAR COMBINATION OF $ U $-STATISTICS FOR A DEGENERATE KERNEL

10.5109/13509 ◽  
2002 ◽  
Vol 34 (1) ◽  
pp. 61-73
Author(s):  
Hajime Yamato ◽  
Masao Kondo
Keyword(s):  
Rate Of Convergence ◽  
Linear Combination ◽  
Degenerate Kernel ◽  
Convergence In Distribution ◽  
U Statistics

Rates of Poisson convergence for U-statistics

1979 ◽  
Vol 16 (2) ◽  
pp. 428-432 ◽  
Author(s):  
T. C. Brown ◽  
B. W. Silverman
Keyword(s):  
Rate Of Convergence ◽  
Limit Theorems ◽  
Plane Region ◽  
U Statistics ◽  
Poisson Limit ◽  
Special Case

Poisson limit theorems for U-statistics are studied. A general rate of convergence is obtained; this rate is improved for the special case where the U-statistic arises from the consideration of distances between uniformly distributed points in a well-behaved plane region.

Mixing rates for Brownian motion in a convex polyhedron

1990 ◽  
Vol 27 (2) ◽  
pp. 259-268 ◽  
Author(s):  
Peter Matthews
Keyword(s):  
Brownian Motion ◽  
Rate Of Convergence ◽  
Convex Polyhedron ◽  
Upper Bounds ◽  
Convergence In Distribution ◽  
Convex Polyhedral ◽  
Variation Distance ◽  
Mixing Rates

For Brownian motion on a convex polyhedral subset of a sphere or torus, the rate of convergence in distribution to uniformity is studied. The main result is a method to take a Markov coupling on the full sphere or torus and create a faster coupling on the convex polyhedral subset. Upper bounds on variation distance are computed, and applications are discussed.

scholarly journals Quasi U-statistics of innite order and applications to the subgroup decomposition of some diversity measures

2014 ◽  
Vol 8 (2) ◽  
pp. 285
Author(s):  
Alusio Pinheiro ◽  
Pranab Kumar Sen
Keyword(s):  
Categorical Data ◽  
Hamming Distance ◽  
Regularity Conditions ◽  
Degenerate Kernel ◽  
Central Tendency ◽  
Asymptotically Normal ◽  
U Statistics ◽  
Diversity Measures ◽  
Common Framework ◽  
Order Degenerate

In several applications, information is drawn from quali- tative variables. In such cases, measures of central tendency and dis- persion may be highly inappropriate. Variability for categorical data can be correctly quantied by the so-called diversity measures. These measures can be modied to quantify heterogeneity between groups (or subpopulations). Pinheiro et al. (2005) shows that Hamming distance can be employed in such way and the resulting estimator of hetero- geneity between populations will be asymptotically normal under mild regularity conditions. Pinheiro et al. (2009) proposes a class of weighted U-statistics based on degenerate kernels of degree 2, called quasi U-statistics, with the property of asymptotic normality under suitable conditions. This is generalized to kernels of degree m by Pinheiro et al. (2011). In this work we generalize this class to an innite order degenerate kernel. We then use this powerful tools and the reverse martingale nature of U-statistics to study the asymptotic behavior of a collection of trans- formed classic diversity measures. We are able to estimate them in a common framework instead of the usual individualized estimation procedures. MSC 2000: primary - 62G10; secondary - 62G20, 92D20.

Rates of Poisson convergence for U-statistics

1979 ◽  
Vol 16 (02) ◽  
pp. 428-432 ◽  
Author(s):  
T. C. Brown ◽  
B. W. Silverman
Keyword(s):  
Rate Of Convergence ◽  
Limit Theorems ◽  
Plane Region ◽  
U Statistics ◽  
Poisson Limit ◽  
Special Case

Poisson limit theorems for U-statistics are studied. A general rate of convergence is obtained; this rate is improved for the special case where the U-statistic arises from the consideration of distances between uniformly distributed points in a well-behaved plane region.

Mixing rates for Brownian motion in a convex polyhedron

1990 ◽  
Vol 27 (02) ◽  
pp. 259-268
Author(s):  
Peter Matthews
Keyword(s):  
Brownian Motion ◽  
Rate Of Convergence ◽  
Convex Polyhedron ◽  
Upper Bounds ◽  
Convergence In Distribution ◽  
Convex Polyhedral ◽  
Variation Distance ◽  
Mixing Rates

For Brownian motion on a convex polyhedral subset of a sphere or torus, the rate of convergence in distribution to uniformity is studied. The main result is a method to take a Markov coupling on the full sphere or torus and create a faster coupling on the convex polyhedral subset. Upper bounds on variation distance are computed, and applications are discussed.

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