On the rate of convergence of recursive kernel estimates of probability densities

1988 ◽  
Vol 16 (4) ◽  
pp. 399-409 ◽  
Author(s):  
K. I. Abdul-Al
Keyword(s):  
Rate Of Convergence ◽  
Kernel Estimates ◽  
Probability Densities

scholarly journals Variable window width kernel estimates of probability densities

1992 ◽  
Vol 91 (1) ◽  
pp. 133-133
Author(s):  
Peter Hall ◽  
J. S. Marron
Keyword(s):  
Kernel Estimates ◽  
Window Width ◽  
Probability Densities ◽  
Variable Window

scholarly journals Improved Variable Window Kernel Estimates of Probability Densities

1995 ◽  
Vol 23 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Peter Hall ◽  
Tien Chung Hu ◽  
J. S. Marron
Keyword(s):  
Kernel Estimates ◽  
Probability Densities ◽  
Variable Window

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.

The rate of convergence for quadratic forms

1997 ◽  
Vol 37 (3) ◽  
pp. 191-206
Author(s):  
A. Basalykas
Keyword(s):  
Rate Of Convergence ◽  
Quadratic Forms

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems

2020 ◽  
Vol 20 (4) ◽  
pp. 783-798
Author(s):  
Shukai Du ◽  
Nailin Du
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Convergence Conditions ◽  
Principal Angles ◽  
Factorization Formula ◽  
Ill Posed

AbstractWe give a factorization formula to least-squares projection schemes, from which new convergence conditions together with formulas estimating the rate of convergence can be derived. We prove that the convergence of the method (including the rate of convergence) can be completely determined by the principal angles between {T^{\dagger}T(X_{n})} and {T^{*}T(X_{n})}, and the principal angles between {X_{n}\cap(\mathcal{N}(T)\cap X_{n})^{\perp}} and {(\mathcal{N}(T)+X_{n})\cap\mathcal{N}(T)^{\perp}}. At the end, we consider several specific cases and examples to further illustrate our theorems.

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