Lindeberg condition

2019 ◽  
pp. 51-56
Keyword(s):  
Lindeberg Condition

VICTORIA transform, RESPECT and REFORM methods for the proof of the G-Elliptic Law under G-Lindeberg condition and twice stochastic condition for the variances and covariances of the entries of some random matrices

2020 ◽  
Vol 28 (2) ◽  
pp. 131-162
Author(s):  
Vyacheslav L. Girko
Keyword(s):  
Random Matrices ◽  
Random Matrix ◽  
Lindeberg Condition

AbstractThe G-Elliptic law under the G-Lindeberg condition for the independent pairs of the entries of a random matrix is proven.

Donsker’s fuzzy invariance principle under the Lindeberg condition

2021 ◽  
Vol 71 (2) ◽  
pp. 439-454
Author(s):  
Roman Urban
Keyword(s):  
Continuous Process ◽  
Unit Interval ◽  
Partial Sums ◽  
Standard Brownian Motion ◽  
Triangular System ◽  
Fuzzy Random Variables ◽  
Support Functions ◽  
Lindeberg Condition ◽  
Fuzzy Setting ◽  
Fuzzy Random

Abstract We prove an analogue of the Donsker theorem under the Lindeberg condition in a fuzzy setting. Specifically, we consider a certain triangular system of d-dimensional fuzzy random variables { X n , i ∗ } , $\begin{array}{} \{X_{n,i}^*\}, \end{array}$ n ∈ ℕ and i = 1, 2, …, kn , which take as their values fuzzy vectors of compact and convex α-cuts. We show that an appropriately normalized and interpolated sequence of partial sums of the system may be associated with a time-continuous process defined on the unit interval t ∈ [0, 1] which, under the assumption of the Lindeberg condition, tends in distribution to a standard Brownian motion in the space of support functions.

𝑉-law for random block matrices under the generalized Lindeberg condition

2019 ◽  
Vol 27 (3) ◽  
pp. 177-198
Author(s):  
Vyacheslav L. Girko
Keyword(s):  
Random Matrices ◽  
Stochastic Matrix ◽  
Block Matrices ◽  
Lindeberg Condition ◽  
Random Block ◽  
Random Block Matrices

Abstract The V-law under generalized Lindeberg condition for the independent blocks of random matrices having double stochastic matrix of covariances and different expectations of their array is proven.

V-density for eigenvalues of random block matrices with independent blocks whose entries have different variances and expectations

2019 ◽  
Vol 27 (3) ◽  
pp. 161-165
Author(s):  
Vyacheslav L. Girko ◽  
L. D. Shevchuk
Keyword(s):  
Random Matrices ◽  
Block Matrices ◽  
Lindeberg Condition ◽  
Random Block ◽  
Random Block Matrices

Abstract V-density under Lindeberg condition for the independent blocks of random matrices having different variances and expectations is found.

scholarly journals On Lindeberg-Feller Limit Theorem

2019 ◽  
Vol 485 (5) ◽  
pp. 548-552 ◽  
Author(s):  
E. L. Presman ◽  
Sh. K. Formanov
Keyword(s):  
Limit Theorem ◽  
Classical Setting ◽  
Lindeberg Condition

In the Lindeberg-Feller theorem, the Lindeberg condition is present. The fulfillment of this condition must be checked for any ε > 0. We formulae a new condition in terms of some generalization of moments of order 2 + α, which does not depend on ε, and show that this condition is equivalent to the Lindeberg condition, and if this condition is valid for some α > 0 then it is valid for any α > 0. In the non-classical setting (in the absence of conditions of a uniform infinitely smallness) V.I. Rotar formulated an analogue of the Lindeberg condition in terms of the second pseudo-moments. The paper presents the same modification of Rotar`s condition, which does not depend on ε. In addition, we discuss variants of the simple proofs of theorems of Lindeberg-Feller and Rotar and some related inequalities.

The central limit theorem for m-dependent variables

1955 ◽  
Vol 51 (1) ◽  
pp. 92-95 ◽  
Author(s):  
P. H. Diananda
Keyword(s):  
Standard Deviation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Sufficient Conditions ◽  
The Central Limit Theorem ◽  
Lindeberg Condition ◽  
Dependent Variables ◽  
Basic Ideas

In a previous paper (4) central limit theorems were obtained for sequences of m-dependent random variables (r.v.'s) asymptotically stationary to second order, the sufficient conditions being akin to the Lindeberg condition (3). In this paper similar theorems are obtained for sequences of m-dependent r.v.'s with bounded variances and with the property that for large n, where s′n is the standard deviation of the nth partial sum of the sequence. The same basic ideas as in (4) are used, but the proofs have been simplified. The results of this paper are examined in relation to earlier ones of Hoeffding and Robbins(5) and of the author (4). The cases of identically distributed r.v.'s and of vector r.v.'s are mentioned.

Encyclopedia of Statistical Sciences. Vol. 5: Lindeberg Condition to Multitrait-Multimethod Matrices.

Biometrics ◽  
1986 ◽  
Vol 42 (2) ◽  
pp. 451 ◽  
Author(s):  
S. Berg ◽  
S. Kotz ◽  
N. L. Johnson ◽  
C. B. Read
Keyword(s):  
Lindeberg Condition

The Classical Central Limit Theorem

2021 ◽  
pp. 520-547
Author(s):  
James Davidson
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Stable Convergence ◽  
Random Sums ◽  
The Central Limit Theorem ◽  
Lindeberg Condition

In this chapter, the first approach is made to establishing the convergence of scaled random sums, considering independent sequences. The classic Lindeberg–Lévy, Khinchine, Lindeberg–Feller, and Liapunov theorems are proved. The main focus is on the treatment of heterogeneous summands, applying the Lindeberg condition, and extensions are given to allow trending (growing or shrinking) variances. The final sections review cases of the central limit theorem under non-standard conditions and α‎-stable convergence.

Sign in / Sign up

Export Citation Format

Share Document