scholarly journals Exact rate of convergence of the expected $W_{2}$ distance between the empirical and true Gaussian distribution

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Philippe Berthet ◽  
Jean Claude Fort
Keyword(s):  
Rate Of Convergence ◽  
Gaussian Distribution ◽  
Exact Rate Of Convergence

scholarly journals On Lagrange interpolation with equally spaced nodes

2000 ◽  
Vol 62 (3) ◽  
pp. 357-368 ◽  
Author(s):  
Michael Revers
Keyword(s):  
Rate Of Convergence ◽  
Lagrange Interpolation ◽  
End Points ◽  
Quantitative Version ◽  
Equidistant Nodes ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials ◽  
Exact Rate Of Convergence

A well-known result due to S.N. Bernstein is that sequence of Lagrange interpolation polynomials for |x| at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In this paper we present a quantitative version concerning the divergence behaviour of the Lagrange interpolants for |x|3 at equidistant nodes. Furthermore, we present the exact rate of convergence for the interpolatory parabolas at the point zero.

On the exact rate of convergence of frequencies of digits and local dimensions of multinomial measures

2015 ◽  
Vol 159 (3) ◽  
pp. 387-403
Author(s):  
L. OLSEN
Keyword(s):  
Rate Of Convergence ◽  
Normal Numbers ◽  
Hausdorff Dimensions ◽  
Exact Rate Of Convergence

AbstractWe study the Hausdorff dimensions of certain sets of non-normal numbers defined in terms of the exact rate of convergence of digits in theirN-adic expansions. As an application of our results we analyse the rate of convergence of local dimensions of multinomial measures.

On transient behaviour of a nearest-neighbour birth-death process on a lattice

1994 ◽  
Vol 31 (2) ◽  
pp. 549-553 ◽  
Author(s):  
Boris L. Granovsky ◽  
Liat Rozov
Keyword(s):  
Steady State ◽  
Rate Of Convergence ◽  
Death Process ◽  
Nearest Neighbour ◽  
Regular Lattice ◽  
Transient Behaviour ◽  
Coverage Function ◽  
The Mean ◽  
Exact Rate Of Convergence

We provide the explicit expression for the mean coverage function of a generalized voter model on a regular lattice and establish a characterization of the class of the above processes. As a result, we derive the exact rate of convergence of the considered processes to the steady state. We also prove the existence of different processes with the same mean coverage function on a given lattice.

scholarly journals Multipoint Padé-Type Approximants. Exact Rate of Convergence

1997 ◽  
Vol 14 (2) ◽  
pp. 259-272 ◽  
Author(s):  
F. Cala Rodriguez ◽  
G. López Lagomasino
Keyword(s):  
Rate Of Convergence ◽  
Exact Rate Of Convergence

scholarly journals An Edgeworth Expansion for the Ratio of Two Functionals of Gaussian Fields and Optimal Berry–Esseen Bounds

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2223
Author(s):  
Yoon-Tae Kim ◽  
Hyun-Suk Park
Keyword(s):  
Differential Equations ◽  
Rate Of Convergence ◽  
Edgeworth Expansion ◽  
Normal Approximation ◽  
Gaussian Fields ◽  
Kolmogorov Distance ◽  
Likelihood Estimator ◽  
Infinite Dimensional ◽  
A New Technique ◽  
Exact Rate Of Convergence

This paper is concerned with the rate of convergence of the distribution of the sequence {Fn/Gn}, where Fn and Gn are each functionals of infinite-dimensional Gaussian fields. This form very frequently appears in the estimation problem of parameters occurring in Stochastic Differential Equations (SDEs) and Stochastic Partial Differential Equations (SPDEs). We develop a new technique to compute the exact rate of convergence on the Kolmogorov distance for the normal approximation of Fn/Gn. As a tool for our work, an Edgeworth expansion for the distribution of Fn/Gn, with an explicitly expressed remainder, will be developed, and this remainder term will be controlled to obtain an optimal bound. As an application, we provide an optimal Berry–Esseen bound of the Maximum Likelihood Estimator (MLE) of an unknown parameter appearing in SDEs and SPDEs.

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