The strong uniform convergence of multivariate variable kernel estimates

1986 ◽  
Vol 14 (3) ◽  
pp. 211-220 ◽  
Author(s):  
Luc Devroye ◽  
Clark S. Penrod
Keyword(s):  
Uniform Convergence ◽  
Kernel Estimates ◽  
Variable Kernel ◽  
Strong Uniform Convergence

scholarly journals Statistical Convergence in Function Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Agata Caserta ◽  
Giuseppe Di Maio ◽  
Ljubiša D. R. Kočinac
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Statistical Approach ◽  
Metric Spaces ◽  
Function Spaces ◽  
Strong Uniform Convergence ◽  
Convergence Of Sequences

We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.

scholarly journals Strong Proximal Continuity and Convergence

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Agata Caserta ◽  
Roberto Lucchetti ◽  
Som Naimpally
Keyword(s):  
Uniform Convergence ◽  
Uniform Continuity ◽  
Strong Continuity ◽  
Uniform Spaces ◽  
Constrained Problems ◽  
Strong Uniform Convergence ◽  
Proximity Spaces

In several situations the notion of uniform continuity can be strengthened to strong uniform continuity to produce interesting properties, especially in constrained problems. The same happens in the setting of proximity spaces. While a parallel theory for uniform and strong uniform convergence was recently developed, and a notion of proximal convergence is present in the literature, the notion of strong proximal convergence was never considered. In this paper, we propose several possible convergence notions, and we provide complete comparisons among these concepts and the notion of strong uniform convergence in uniform spaces. It is also shown that in particularly meaningful classes of functions these notions are equivalent and can be considered as natural definitions of strong proximal convergence. Finally we consider a function acting between two proximity spaces and we connect its continuity/strong continuity to convergence in the respective hyperspaces of a natural functor associated to the function itself.

Variable Kernel Estimates of Multivariate Densities

Technometrics ◽  
1977 ◽  
Vol 19 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Leo Breiman ◽  
William Meisel ◽  
Edward Purcell
Keyword(s):  
Kernel Estimates ◽  
Variable Kernel
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