scholarly journals Adaptive Wavelet Estimation of a Biased Density for Strongly Mixing Sequences

2011 ◽  
Vol 2011 ◽  
pp. 1-21
Author(s):  
Christophe Chesneau
Keyword(s):  
Wide Class ◽  
Upper Bound ◽  
Hard Thresholding ◽  
Wavelet Estimation ◽  
Adaptive Wavelet ◽  
Wavelet Estimator ◽  
Strongly Mixing ◽  
Mean Integrated Square Error ◽  
Mixing Sequences ◽  
Class Of Functions

The estimation of a biased density for exponentially strongly mixing sequences is investigated. We construct a new adaptive wavelet estimator based on a hard thresholding rule. We determine a sharp upper bound of the associated mean integrated square error for a wide class of functions.

scholarly journals Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables

1997 ◽  
Vol 10 (1) ◽  
pp. 3-20 ◽  
Author(s):  
Shan Sun ◽  
Ching-Yuan Chiang
Keyword(s):  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Random Variables ◽  
Distribution Functions ◽  
Limiting Behavior ◽  
U Statistics ◽  
Strongly Mixing ◽  
Almost Sure Representation ◽  
Mixing Sequences ◽  
Empirical Distribution Functions

We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic Fˆn(Un) for a class of strongly mixing sequences of random variables {Xi,i≥1}. Stationarity is not assumed. Here Fˆn is the perturbed empirical distribution function and Un is a U-statistic based on X1,…,Xn.

EXISTENCE OF STRONG TRACES FOR GENERALIZED SOLUTIONS OF MULTIDIMENSIONAL SCALAR CONSERVATION LAWS

2005 ◽  
Vol 02 (04) ◽  
pp. 885-908 ◽  
Author(s):  
E. YU. PANOV
Keyword(s):  
Wide Class ◽  
Conservation Law ◽  
Generalized Solutions ◽  
Flux Vector ◽  
Scalar Conservation Laws ◽  
Generalized Entropy ◽  
Scalar Conservation Law ◽  
Nondegeneracy Conditions ◽  
Scalar Conservation ◽  
Class Of Functions

In the half-space t > 0 a multidimensional scalar conservation law with only continuous flux vector is considered. For the wide class of functions including generalized entropy sub- and super-solutions to this equation, we prove existence of the strong trace on the initial hyperspace t = 0. No nondegeneracy conditions on the flux are required.

scholarly journals Reflection of Functions and Linear Prognosis

2021 ◽  
Author(s):  
Andrei Valerianovich Pavlov
Keyword(s):  
Linear Transformation ◽  
Wide Class ◽  
Symmetric Case ◽  
Regular Functions ◽  
Class Of Functions

Periodicity of wide class of functions as a result of reflection of even and arbitrary regular functions is proved. By consideration of new scalar work in space of linear shell of initial n vectors the equivalence of values of two different scalar productions is proved. The example of linear transformation is considered on plane for the symmetric case, resulting in possibility to make to use the orthogonal sides of rhombus at projection on the plane of its parties.

Wavelet pointwise estimations under multiplicative censoring

2020 ◽  
Vol 18 (04) ◽  
pp. 2050020
Author(s):  
Jinru Wang ◽  
Zhenming Zhang ◽  
Xue Zhang ◽  
Xiaochen Zeng
Keyword(s):  
Upper Bound ◽  
Convergence Rates ◽  
Convergence Order ◽  
Asymptotic Convergence ◽  
Threshold Method ◽  
Hölder Spaces ◽  
Wavelet Estimator ◽  
Mixture Density ◽  
Multiplicative Censoring ◽  
Holder Spaces

In this paper, we investigate the wavelet-based estimators of a kind of censored mixture density and discuss their pointwise asymptotic convergence rates over Hölder spaces. We first consider the linear wavelet estimator and give its upper bound. However, the linear one is nonadaptive and not applicable since it is related to the unknown space parameter. Finally, we use the hard threshold method to explore adaptive nonlinear wavelet estimator and obtain the same convergence order as the linear one up to a logarithmic penalty.

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