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.

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.

Rate of Convergence in Density Estimation Using Neural Networks

1996 ◽  
Vol 8 (5) ◽  
pp. 1107-1122 ◽  
Author(s):  
Dharmendra S. Modha ◽  
Elias Masry
Keyword(s):  
Neural Networks ◽  
Probability Density Function ◽  
Probability Density ◽  
Rate Of Convergence ◽  
Density Function ◽  
Density Estimation ◽  
Exponential Family ◽  
Density Estimator ◽  
Estimation Scheme ◽  
Hidden Layer

Given N i.i.d. observations {Xi}Ni=1 taking values in a compact subset of Rd, such that p* denotes their common probability density function, we estimate p* from an exponential family of densities based on single hidden layer sigmoidal networks using a certain minimum complexity density estimation scheme. Assuming that p* possesses a certain exponential representation, we establish a rate of convergence, independent of the dimension d, for the expected Hellinger distance between the proposed minimum complexity density estimator and the true underlying density p*.

scholarly journals Pointwise Optimality of Wavelet Density Estimation for Negatively Associated Biased Sample

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 176 ◽  
Author(s):  
Renyu Ye ◽  
Xinsheng Liu ◽  
Yuncai Yu
Keyword(s):  
Density Estimation ◽  
Mean Squared Error ◽  
Density Estimator ◽  
Wavelet Method ◽  
Wavelet Estimator ◽  
Negatively Associated ◽  
Squared Error ◽  
Wavelet Density Estimation ◽  
The Mean ◽  
Block Thresholding

This paper focuses on the density estimation problem that occurs when the sample is negatively associated and biased. We constructed a block thresholding wavelet estimator to recover the density function from the negatively associated biased sample. The pointwise optimality of this wavelet density estimation is shown as L p ( 1 ≤ p < ∞ ) risks over Besov space. To validate the effectiveness of the block thresholding wavelet method, we provide some examples and implement the numerical simulations. The results indicate that our block thresholding wavelet density estimator is superior in terms of the mean squared error (MSE) when comparing with the nonlinear wavelet density estimator.

Computational Models of Bio Heuristics Based on Physical and Cognitive Processes (Review)

2021 ◽  
Vol 27 (11) ◽  
pp. 563-574
Author(s):  
V. V. Kureychik ◽  
◽  
S. I. Rodzin ◽  
Keyword(s):  
Computational Complexity ◽  
Convergence Rate ◽  
Rate Of Convergence ◽  
Cognitive Processes ◽  
Computational Models ◽  
Optimization Problems ◽  
Search Space ◽  
Experimental Results ◽  
Software Implementation ◽  
Minimum Total Length

Computational models of bio heuristics based on physical and cognitive processes are presented. Data on such characteristics of bio heuristics (including evolutionary and swarm bio heuristics) are compared.) such as the rate of convergence, computational complexity, the required amount of memory, the configuration of the algorithm parameters, the difficulties of software implementation. The balance between the convergence rate of bio heuristics and the diversification of the search space for solutions to optimization problems is estimated. Experimental results are presented for the problem of placing Peco graphs in a lattice with the minimum total length of the graph edges.

scholarly journals Rate of convergence for periodic homogenization of convex Hamilton–Jacobi equations in one dimension

2021 ◽  
Vol 121 (2) ◽  
pp. 171-194
Author(s):  
Son N.T. Tu
Keyword(s):  
Rate Of Convergence ◽  
Classical Mechanics ◽  
One Dimension ◽  
Separable Potential ◽  
Periodic Homogenization ◽  
Periodic Functions ◽  
Effective Equation ◽  
Optimal Rate Of Convergence ◽  
Jacobi Equations ◽  
Hamilton Jacobi Equation

Let u ε and u be viscosity solutions of the oscillatory Hamilton–Jacobi equation and its corresponding effective equation. Given bounded, Lipschitz initial data, we present a simple proof to obtain the optimal rate of convergence O ( ε ) of u ε → u as ε → 0 + for a large class of convex Hamiltonians H ( x , y , p ) in one dimension. This class includes the Hamiltonians from classical mechanics with separable potential. The proof makes use of optimal control theory and a quantitative version of the ergodic theorem for periodic functions in dimension n = 1.

Nonparametric Least Squares Mixture Density Estimation

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Chew-Seng Chee
Keyword(s):  
Least Squares ◽  
Density Estimation ◽  
Least Squares Method ◽  
Bandwidth Selection ◽  
Estimation Problem ◽  
Density Estimator ◽  
Mixing Distribution ◽  
Mixture Density ◽  
Integrated Squared Error ◽  
Nonparametric Mixture Model

In this paper, we consider using nonparametric mixtures for density estimation. The mixture density estimation problem simply reduces to the problem of estimating a mixing distribution in the nonparametric mixture model. We focus on the least squares method for mixture density estimation problem. In a simulation experiment, the performance of the least squares mixture density estimator (MDE) and the kernel density estimator (KDE) is assessed by the mean integrated squared error. The performance improvement of MDE over KDE for some common densities is achieved by using cross-validation method for bandwidth selection.

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