Asymptotic properties of nonparametric regression for long memory random fields

2010 ◽  
Vol 140 (3) ◽  
pp. 837-850 ◽  
Author(s):  
Lihong Wang ◽  
Haiyan Cai
Keyword(s):  
Nonparametric Regression ◽  
Random Fields ◽  
Long Memory ◽  
Asymptotic Properties

scholarly journals Cramér type moderate deviations for random fields

2019 ◽  
Vol 56 (01) ◽  
pp. 223-245 ◽  
Author(s):  
Aleksandr Beknazaryan ◽  
Hailin Sang ◽  
Yimin Xiao
Keyword(s):  
Random Field ◽  
Nonparametric Regression ◽  
Random Fields ◽  
Long Memory ◽  
Moderate Deviation ◽  
Moderate Deviations ◽  
Partial Sums ◽  
Field Errors

AbstractWe study the Cramér type moderate deviation for partial sums of random fields by applying the conjugate method. The results are applicable to the partial sums of linear random fields with short or long memory and to nonparametric regression with random field errors.

scholarly journals On nonparametric regression for bivariate circular long-memory time series

2021 ◽  
Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Long Range ◽  
Long Memory ◽  
Regression Function ◽  
Confidence Bands ◽  
Long Range Dependence ◽  
Asymptotic Results ◽  
Memory Time ◽  
Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

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 The limiting spectral distribution in terms of spectral density

2016 ◽  
Vol 05 (01) ◽  
pp. 1650003 ◽  
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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