scholarly journals Weak convergence of the least concave majorant of estimators for a concave distribution function

2017 ◽  
Vol 11 (2) ◽  
pp. 3841-3870 ◽  
Author(s):  
Brendan K. Beare ◽  
Zheng Fang
Keyword(s):  
Distribution Function ◽  
Weak Convergence ◽  
Least Concave Majorant

scholarly journals Weak Convergence of the Rao-Blackwell Estimator of a Distribution Function

1977 ◽  
Vol 5 (3) ◽  
pp. 500-510 ◽  
Author(s):  
B. B. Bhattacharyya ◽  
P. K. Sen
Keyword(s):  
Distribution Function ◽  
Weak Convergence

The time constant of first-passage percolation on the square lattice

1980 ◽  
Vol 12 (4) ◽  
pp. 864-879 ◽  
Author(s):  
J. Theodore Cox
Keyword(s):  
Distribution Function ◽  
Weak Convergence ◽  
Time Constant ◽  
Square Lattice ◽  
First Passage Percolation ◽  
First Passage ◽  
Underlying Distribution

Let μ (F) be the time constant of first-passage percolation on the square lattice with underlying distribution function F. Two theorems are presented which show, under some restrictions, that μ varies continuously in F with respect to weak convergence. These results are improvements of existing continuity theorems.

scholarly journals On the Limiting Behaviour of the Empirical Kernel Distribution Function

1983 ◽  
Vol 32 (1-2) ◽  
pp. 1-8 ◽  
Author(s):  
Pranab Kumar Sen
Keyword(s):  
Distribution Function ◽  
Weak Convergence ◽  
Empirical Process ◽  
Type Result ◽  
Cantelli Lemma ◽  
Limiting Behaviour

For an estimable parameter of degree m(⩾ 1), Glivenko-Cantelli lemma type result for the empirical kernel distribution and weak convergence of the related empirical process are studied. Some statistical applications of these results are also considered.

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