Semiparametric nonlinear log-periodogram regression estimation for perturbed stationary anisotropic long memory random fields

2021 ◽

Author(s):

Han-Mai Lin

Keyword(s):

Invariance Principle ◽

Random Fields ◽

Long Memory ◽

Sufficient Conditions ◽

Weak Invariance Principle ◽

Weak Invariance ◽

The Central Limit Theorem ◽

Projective Criteria ◽

Stationary Random Fields ◽

Do So

In this paper, we study the central limit theorem (CLT) and its weak invariance principle (WIP) for sums of stationary random fields non-necessarily adapted, under different normalizations. To do so, we first state sufficient conditions for the validity of a suitable ortho-martingale approximation. Then, with the help of this approximation, we derive projective criteria under which the CLT as well as the WIP hold. These projective criteria are in the spirit of Hannan’s condition and are well adapted to linear random fields with ortho-martingale innovations and which exhibit long memory.

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Long memory random fields

Lecture Notes in Statistics - Dependence in Probability and Statistics ◽

10.1007/0-387-36062-x_9 ◽

2006 ◽

pp. 195-220 ◽

Cited By ~ 10

Author(s):

Frédéric Lavancier

Keyword(s):

Random Fields ◽

Long Memory

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On estimation of regression coefficients of long memory random fields observed on the arrays

Random Operators and Stochastic Equations ◽

10.1515/rose.1998.6.1.61 ◽

1998 ◽

Vol 6 (1) ◽

Cited By ~ 3

Author(s):

N. N. LEONENKO ◽

M. BENŠIĆ

Keyword(s):

Random Fields ◽

Long Memory ◽

Regression Coefficients

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The limiting spectral distribution in terms of spectral density

Random Matrices Theory and Application ◽

10.1142/s2010326316500039 ◽

2016 ◽

Vol 05 (01) ◽

pp. 1650003 ◽

Cited By ~ 2

Author(s):

Costel Peligrad ◽

Magda Peligrad

Keyword(s):

Spectral Density ◽

Rate Of Convergence ◽

Large Class ◽

Random Fields ◽

Long Memory ◽

Spectral Distribution ◽

Complete Solution ◽

Gaussian Random Fields ◽

Stieltjes Transform ◽

Counting Measure

For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists and we describe it via an equation satisfied by its Stieltjes transform. No rate of convergence to zero of correlations is imposed, therefore the process is allowed to have long memory. In particular, if the symmetrized matrices are constructed from stationary Gaussian random fields which have spectral density, the result of this paper gives a complete solution to the limiting eigenvalue distribution. More generally, for matrices whose entries are functions of independent and identically distributed random variables the result also holds.

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