The rate of convergence and error distribution of Galerkin approximations to eigenvalues in underwater acoustics

2013 ◽  
Vol 133 (5) ◽  
pp. 3529-3529
Author(s):  
Richard B. Evans
Keyword(s):  
Rate Of Convergence ◽  
Underwater Acoustics ◽  
Error Distribution ◽  
Galerkin Approximations

Influence of design on the rate of convergence to normality in L1 regression

1989 ◽  
Vol 106 (2) ◽  
pp. 355-368 ◽  
Author(s):  
Peter Hall ◽  
A. H. Welsh
Keyword(s):  
Convergence Rate ◽  
Rate Of Convergence ◽  
Edgeworth Expansion ◽  
Sufficient Conditions ◽  
Error Distribution ◽  
Necessary And Sufficient Conditions ◽  
Moment Condition ◽  
Regression Problem ◽  
Design Variables ◽  
Necessary And Sufficient

AbstractWe provide a concise account of the influence of design variables on the convergence rate in an L1 regression problem. In particular, we show that the convergence rate may be characterized precisely in terms of third and fourth moments of the design variables. This result leads to necessary and sufficient conditions on the design for the Berry-Esseen rate to be achieved. We also show that a moment condition on the error distribution is necessary and sufficient for a non-uniform Berry-Esseen theorem, and that an Edgeworth expansion is possible if the design points are not too clumped.

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

Sign in / Sign up

Export Citation Format

Share Document