Multivariate wavelet estimators for weakly dependent processes: strong consistency rate

Allaoui, Soumaya; Bouzebda, Salim; Liu, Jicheng

doi:10.1080/03610926.2022.2061715

Cited by 8 publications

(2 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other side, the Galerkin and the Petrov-Galerkin methods had been used to approximate the solution of nonlinear integral equation of the Urysohn type by work for [9]. After that, [1] produced another result about convergence theory by proving the strong uniform consistency properties of the non parametric linear wavelet-based estimators, over compact subsets of R d , the corresponding rates of convergence were determinate. Liu [6] provided a fast convergent approximation to the nonlinear hyperbolic Schrödinger equations, the efficient method were presented precision by calculated the maximum error norm and the experimental rate of convergence.…”

Section: Related Workmentioning

confidence: 99%

The Convergence of Operator With Rapidly Decreasing Wavelet Functions

Shamsah¹,

Ahmedov²,

Kılıçman³

et al. 2022

MJMS

View full text Add to dashboard Cite

The expansion of (2D) wavelet functions with respect to Lp(R2) space converging almost everywhere for 1<p<∞ throughout the length of the Lebesgue set points of space functions is investigated in this research. The convergence is established by assuming some wavelet function minimal regularity ψj1,j2,k1,k2 under the current description of the wavelet projection operator known as 2D Hard Sampling Operator. Note that the feature of fast decline in 2D is derived here. Another condition is used, for instance, the wavelet expansion's boundedness under the Hard Sampling Operator. The bound (limit) is governed in magnitude with respect to the maximal equality of the Hardy-Littlewood maximal operator. Some ideas presented in this work are to find a new method to prove the convergence theory for a new type of conditional wavelet operator. Propose some conditions for wavelets functions and their expansion can support the operator to be convergence. It also performs a comparison with the identity convergent operator is our method for achieving this convergence.

show abstract

Section: Related Workmentioning

confidence: 99%

The Convergence of Operator With Rapidly Decreasing Wavelet Functions

Shamsah¹,

Ahmedov²,

Kılıçman³

et al. 2022

MJMS

View full text Add to dashboard Cite

show abstract

“…In detail, [31] discusses the estimation of partial derivatives of a multivariate probability density function in the presence of additive noise. We could consult [32,33] for the most recent information on this subject. Using the independent and identically distributed paradigm, [34] examined density and regression estimation issues unique to functional data.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes

Didi

Bouzebda

2022

Mathematics

Self Cite

View full text Add to dashboard Cite

In this study, we look at the wavelet basis for nonparametric estimation of density and regression functions for continuous functional stationary processes in Hilbert space. The mean integrated squared error for a small subset is established. We employ a martingale approach to obtain the asymptotic properties of these wavelet estimators. These findings are established under rather broad assumptions. All we assume about the data is that it is ergodic, but beyond that, we make no assumptions. In this paper, the mean integrated squared error findings in the independence or mixing setting were generalized to the ergodic setting. The theoretical results presented in this study are (or will be) valuable resources for various cutting-edge functional data analysis applications. Applications include conditional distribution, conditional quantile, entropy, and curve discrimination.

show abstract