scholarly journals Rates of convergence for the distance between distribution function estimators

Metrika ◽  
1986 ◽  
Vol 33 (1) ◽  
pp. 197-202 ◽  
Author(s):  
D. D. Boos
Keyword(s):  
Distribution Function ◽  
Rates Of Convergence

scholarly journals Rates of convergence for U-Statistics with varying kernels

1980 ◽  
Vol 21 (1) ◽  
pp. 1-5 ◽  
Author(s):  
N.C. Weber
Keyword(s):  
Distribution Function ◽  
Rates Of Convergence ◽  
U Statistics ◽  
Standard Normal Variable ◽  
Normal Variable ◽  
Standard Normal

Let Un be a U-statistic whose kernel depends on the size n of the sample under consideration. It is shown that when Un is suitably normalised its distribution function differs in Lp norm from the distribution function of a standard normal variable by a term of O(n-½).

scholarly journals Regeneration and general Markov chains

1994 ◽  
Vol 7 (3) ◽  
pp. 357-371 ◽  
Author(s):  
Vladimir V. Kalashnikov
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Quantitative Analysis ◽  
Markov Chains ◽  
Rates Of Convergence ◽  
Regenerative Process ◽  
Wide Sense ◽  
Visit Time ◽  
Finite Approximations

Ergodicity, continuity, finite approximations and rare visits of general Markov chains are investigated. The obtained results permit further quantitative analysis of characteristics, such as, rates of convergence, continuity (measured as a distance between perturbed and non-perturbed characteristics), deviations between Markov chains, accuracy of approximations and bounds on the distribution function of the first visit time to a chosen subset, etc. The underlying techniques use the embedding of the general Markov chain into a wide sense regenerative process with the help of splitting construction.

A property of longtailed distributions

1984 ◽  
Vol 21 (1) ◽  
pp. 80-87 ◽  
Author(s):  
Paul Embrechts ◽  
Edward Omey
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Renewal Theory ◽  
Rates Of Convergence ◽  
Risk Theory

We investigate sufficient conditions so that is subexponential. Here F is a distribution function on [0, ∞[, with finite mean. Some applications to risk theory and rates of convergence in renewal theory are given.

A property of longtailed distributions

1984 ◽  
Vol 21 (01) ◽  
pp. 80-87 ◽  
Author(s):  
Paul Embrechts ◽  
Edward Omey
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Renewal Theory ◽  
Rates Of Convergence ◽  
Risk Theory

We investigate sufficient conditions so that is subexponential. Here F is a distribution function on [0, ∞[, with finite mean. Some applications to risk theory and rates of convergence in renewal theory are given.

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