Sufficient conditions for asymptotic normality of sums of values of discrete random fields, dependent in strips

1978 ◽  
Vol 23 (5) ◽  
pp. 400-403 ◽  
Author(s):  
L. A. Zolotukhina ◽  
V. N. Chugueva
Keyword(s):  
Asymptotic Normality ◽  
Random Fields ◽  
Sufficient Conditions

scholarly journals Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields

2011 ◽  
Vol 2011 ◽  
pp. 1-35
Author(s):  
Sidi Ali Ould Abdi ◽  
Sophie Dabo-Niang ◽  
Aliou Diop ◽  
Ahmedoune Ould Abdi
Keyword(s):  
Asymptotic Normality ◽  
Random Fields ◽  
Quantile Function ◽  
Spatial Process ◽  
Kernel Estimate ◽  
Conditional Quantile ◽  
Conditional Quantile Estimator ◽  
Conditional Quantile Function ◽  
Mixing Sequence ◽  
Explicative Variable

Given a stationary multidimensional spatial process , we investigate a kernel estimate of the spatial conditional quantile function of the response variable given the explicative variable . Asymptotic normality of the kernel estimate is obtained when the sample considered is an -mixing sequence.

On the weak invariance principle for non-adapted stationary random fields under projective criteria

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.

scholarly journals Power in High‐Dimensional Testing Problems

Econometrica ◽  
2019 ◽  
Vol 87 (3) ◽  
pp. 1055-1069 ◽  
Author(s):  
Anders Bredahl Kock ◽  
David Preinerstorfer
Keyword(s):  
Asymptotic Normality ◽  
Sample Size ◽  
Parameter Space ◽  
Sufficient Conditions ◽  
High Dimensional ◽  
Local Asymptotic Normality ◽  
Asymptotic Power ◽  
Asymptotic Size ◽  
Power Of Tests ◽  
Power Enhancement

Fan, Liao, and Yao (2015) recently introduced a remarkable method for increasing the asymptotic power of tests in high‐dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, has uniformly non‐inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied and show the following: In asymptotic regimes where the dimensionality of the parameter space is fixed as sample size increases, there often exist tests that cannot be further improved with the power enhancement principle. However, when the dimensionality of the parameter space increases sufficiently slowly with sample size and a marginal local asymptotic normality (LAN) condition is satisfied, every test with asymptotic size smaller than 1 can be improved with the power enhancement principle. While the marginal LAN condition alone does not allow one to extend the latter statement to all rates at which the dimensionality increases with sample size, we give sufficient conditions under which this is the case.

New models for Markov random fields

1992 ◽  
Vol 29 (04) ◽  
pp. 877-884 ◽  
Author(s):  
Noel Cressie ◽  
Subhash Lele
Keyword(s):  
Random Field ◽  
Conditional Probability ◽  
Markov Random Field ◽  
Random Fields ◽  
Markov Random Fields ◽  
Sufficient Conditions ◽  
Joint Probability ◽  
Probability Models ◽  
Markov Random ◽  
New Models

The Hammersley–Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.

On the asymptotic normality of the number of empty cells in a scheme of group allocation of particles

2014 ◽  
Vol 24 (6) ◽  
Author(s):  
Vladimir P. Chistyakov
Keyword(s):  
Asymptotic Normality ◽  
Sufficient Conditions ◽  
Asymptotic Formulas ◽  
Group Allocation ◽  
Number Of Cells

AbstractThe paper is concerned with a scheme of m-dependent allocation of non-equiprobable groups of particles into cells. It is assumed that the number of groups and the number of cells tend to infinity and are of the same order. Asymptotic formulas for expectation and variance are obtained and sufficient conditions for the asymptotic normality of the number of empty cells in this scheme are formulated.

scholarly journals Asymptotic normality of frequency polygons for random fields

2010 ◽  
Vol 140 (2) ◽  
pp. 502-514 ◽  
Author(s):  
Michel Carbon ◽  
Christian Francq ◽  
Lanh Tat Tran
Keyword(s):  
Asymptotic Normality ◽  
Random Fields ◽  
Frequency Polygons
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