Wavelet thresholding estimation of density derivatives from a negatively associated size-biased sample

2020 ◽  
Vol 18 (03) ◽  
pp. 2050016
Author(s):  
Junlian Xu
Keyword(s):  
Convergence Rate ◽  
Upper Bounds ◽  
Wavelet Thresholding ◽  
Wavelet Estimation ◽  
Wavelet Estimator ◽  
Negatively Associated ◽  
Better Than

This paper considers wavelet estimation for density derivatives based on negatively associated and size-biased data. We provide upper bounds of nonlinear wavelet estimator on [Formula: see text] risk. It turns out that the convergence rate of the nonlinear estimator is better than that of the linear one.

Global L2 error of wavelet density estimator with truncated and strong mixing observations

2014 ◽  
Vol 12 (03) ◽  
pp. 1450033 ◽  
Author(s):  
Yu-Ye Zou ◽  
Han-Ying Liang
Keyword(s):  
Convergence Rate ◽  
Rate Of Convergence ◽  
Density Estimation ◽  
Linear Estimator ◽  
Strong Mixing ◽  
Density Estimator ◽  
Wavelet Thresholding ◽  
Independent Data ◽  
Wavelet Estimator ◽  
Optimal Rate Of Convergence

In this paper, we discuss the global L2-error of the nonlinear wavelet estimator of density in the Besov space [Formula: see text] for the truncation model when the data exhibit strong mixing assumption, and prove that the estimator can achieve the optimal rate of convergence, which is similar to that in the complete and independent data case with term-by-term thresholding of the empirical wavelet coefficients (D. L. Donoho, I. M. Johnstone, G. Kerkyacharian and D. Picard, Density estimation by wavelet thresholding, Ann. Statist.24 (1996) 508–539). In addition, the conclusion shows that the convergence rate of the nonlinear estimator is faster than that of its linear estimator in some range.

DENOISING OF THREE-DIMENSIONAL DATA CUBE USING BIVARIATE WAVELET SHRINKING

2011 ◽  
Vol 25 (03) ◽  
pp. 403-413 ◽  
Author(s):  
GUANGYI CHEN ◽  
TIEN D. BUI ◽  
ADAM KRZYZAK
Keyword(s):  
Spectral Band ◽  
Gaussian White Noise ◽  
Three Dimensional ◽  
Classical Problem ◽  
Data Cube ◽  
Wavelet Thresholding ◽  
3D Data ◽  
Signal Image ◽  
3D Data Cube ◽  
Better Than

The denoising of a natural signal/image corrupted by Gaussian white noise is a classical problem in signal/image processing. However, it is still in its infancy to denoise high dimensional data. In this paper, we extended Sendur and Selesnick's bivariate wavelet thresholding from two-dimensional (2D) image denoising to three-dimensional (3D) data cube denoising. Our study shows that bivariate wavelet thresholding is still valid for 3D data cubes. Experimental results show that bivariate wavelet thresholding on 3D data cube is better than performing 2D bivariate wavelet thresholding on every spectral band separately, VisuShrink, and Chen and Zhu's 3-scale denoising.

Optimization Design of Electromagnetic Devices Using an Enhanced Salp Swarm Algorithm

2021 ◽  
Vol 35 (12) ◽  
pp. 1471-1476
Author(s):  
Houssem Bouchekara ◽  
Mostafa Smail ◽  
Mohamed Javaid ◽  
Sami Shamsah
Keyword(s):  
Optimization Design ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Design Problems ◽  
Salp Swarm Algorithm ◽  
Electromagnetic Devices ◽  
Swarm Algorithm ◽  
Better Than

An Enhanced version of the Salp Swarm Algorithm (SSA) referred to as (ESSA) is proposed in this paper for the optimization design of electromagnetic devices. The ESSA has the same structure as of the SSA with some modifications in order to enhance its performance for the optimization design of EMDs. In the ESSA, the leader salp does not move around the best position with a fraction of the distance between the lower and upper bounds as in the SAA; rather, a modified mechanism is used. The performance of the proposed algorithm is tested on the widely used Loney’s solenoid and TEAM Workshop Problem 22 design problems. The obtained results show that the proposed algorithm is much better than the initial one. Furthermore, a comparison with other well-known algorithms revealed that the proposed algorithm is very competitive for the optimization design of electromagnetic devices.

ON THE QUASI-STATIONARY DISTRIBUTION OF SIS MODELS

2016 ◽  
Vol 30 (4) ◽  
pp. 622-639 ◽  
Author(s):  
Gaofeng Da ◽  
Maochao Xu ◽  
Shouhuai Xu
Keyword(s):  
Stationary Distribution ◽  
Upper Bound ◽  
Hazard Rate ◽  
State Of The Art ◽  
Upper Bounds ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Novel Method ◽  
Better Than ◽  
Quasi Stationary Distribution

In this paper, we propose a novel method for constructing upper bounds of the quasi-stationary distribution of SIS processes. Using this method, we obtain an upper bound that is better than the state-of-the-art upper bound. Moreover, we prove that the fixed point map Φ [7] actually preserves the equilibrium reversed hazard rate order under a certain condition. This allows us to further improve the upper bound. Some numerical results are presented to illustrate the results.

Geometric renewal convergence rates from hazard rates

2001 ◽  
Vol 38 (01) ◽  
pp. 180-194 ◽  
Author(s):  
Kenneth S. Berenhaut ◽  
Robert Lund
Keyword(s):  
Convergence Rate ◽  
Hazard Rate ◽  
Convergence Rates ◽  
Hazard Rates ◽  
Finite Support ◽  
Good Convergence ◽  
Renewal Sequence ◽  
Geometric Convergence ◽  
New Better Than Used ◽  
Better Than

This paper studies the geometric convergence rate of a discrete renewal sequence to its limit. A general convergence rate is first derived from the hazard rates of the renewal lifetimes. This result is used to extract a good convergence rate when the lifetimes are ordered in the sense of new better than used or increasing hazard rate. A bound for the best possible geometric convergence rate is derived for lifetimes having a finite support. Examples demonstrating the utility and sharpness of the results are presented. Several of the examples study convergence rates for Markov chains.

scholarly journals Composite Differential Search Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Bo Liu
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Search Algorithm ◽  
Search Algorithms ◽  
Control Parameters ◽  
Original Algorithm ◽  
New Space ◽  
Random Method ◽  
Better Than

Differential search algorithm (DS) is a relatively new evolutionary algorithm inspired by the Brownian-like random-walk movement which is used by an organism to migrate. It has been verified to be more effective than ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA-ES. In this paper, we propose four improved solution search algorithms, namely “DS/rand/1,” “DS/rand/2,” “DS/current to rand/1,” and “DS/current to rand/2” to search the new space and enhance the convergence rate for the global optimization problem. In order to verify the performance of different solution search methods, 23 benchmark functions are employed. Experimental results indicate that the proposed algorithm performs better than, or at least comparable to, the original algorithm when considering the quality of the solution obtained. However, these schemes cannot still achieve the best solution for all functions. In order to further enhance the convergence rate and the diversity of the algorithm, a composite differential search algorithm (CDS) is proposed in this paper. This new algorithm combines three new proposed search schemes including “DS/rand/1,” “DS/rand/2,” and “DS/current to rand/1” with three control parameters using a random method to generate the offspring. Experiment results show that CDS has a faster convergence rate and better search ability based on the 23 benchmark functions.

scholarly journals On the Hardness of Offline Multi-objective Optimization

2007 ◽  
Vol 15 (4) ◽  
pp. 475-491 ◽  
Author(s):  
Olivier Teytaud
Keyword(s):  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Random Search ◽  
Computational Cost ◽  
Multiobjective Evolutionary Algorithms ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Insight Into ◽  
Better Than

It has been empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. This paper shows that the convergence rate of all comparison-based multi-objective algorithms, for the Hausdorff distance, is not much better than the convergence rate of the random search under certain conditions. The number of objectives must be very moderate and the framework should hold the following assumptions: the objectives are conflicting and the computational cost is lower bounded by the number of comparisons is a good model. Our conclusions are: (i) the number of conflicting objectives is relevant (ii) the criteria based on comparisons with random-search for multi-objective optimization is also relevant (iii) having more than 3-objectives optimization is very hard. Furthermore, we provide some insight into cross-over operators.

ROUTING BALANCED COMMUNICATIONS ON HAMILTON DECOMPOSABLE NETWORKS

2004 ◽  
Vol 14 (03n04) ◽  
pp. 377-385 ◽  
Author(s):  
LADISLAV STACHO ◽  
JOZEF ŠIRÁŇ ◽  
SANMING ZHOU
Keyword(s):  
Wave Length ◽  
Upper Bounds ◽  
Ring Network ◽  
Special Case ◽  
Better Than

In [10] the authors proved upper bounds for the arc-congestion and wave-length number of any permutation demand on a bidirected ring. In this note, we give generalizations of their results in two directions. The first one is that instead of considering only permutation demands we consider any balanced demand, and the second one is that instead of the ring network we consider any Hamilton decomposable network. Thus, we obtain upper bounds (which are best possible in general) for the arc-congestion and wavelength number of any balanced demand on a Hamilton decomposable network. As a special case, we obtain upper bounds on arc- and edge-forwarding indices of Hamilton decomposable networks that are in many cases better than the known ones.

scholarly journals Convergence of a Proximal Point Algorithm for Solving Minimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Abdelouahed Hamdi ◽  
M. A. Noor ◽  
A. A. Mukheimer
Keyword(s):  
Convergence Rate ◽  
Proximal Point Algorithm ◽  
Iterative Scheme ◽  
Point Method ◽  
Proximal Point Method ◽  
Proximal Point ◽  
Minimization Problems ◽  
Estimate Rate ◽  
Proximal Term ◽  
Better Than

We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild assumptions. Furthermore, it is shown that this estimate rate is better than the available ones.

scholarly journals Estimating and Approximating the Total π-Electron Energy of Benzenoid Hydrocarbons

2000 ◽  
Vol 55 (5) ◽  
pp. 507-512 ◽  
Author(s):  
I. Gutman ◽  
J. H. Koolen ◽  
V. Moulto ◽  
M. Parac ◽  
T. Soldatović ◽  
...  
Keyword(s):  
Electron Energy ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Benzenoid Hydrocarbons ◽  
Carbon Carbon Bonds ◽  
Carbon Bonds ◽  
Approximate Formulas ◽  
Better Than

Abstract Lower and upper bounds as well as approximate formulas for the total π-electron energy (E) of benzenoid hydrocarbons are deduced, depending only on the number of carbon atoms (n) and number of carbon-carbon bonds (to). These are better than the several previously known (n, m)-type estimates and approximations for E.

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