Applications of the local-linear method of super-resolution

2002 ◽  
Author(s):  
Evgeni N. Terentiev ◽  
Nikolai E. Terentiev ◽  
Fedor V. Shugaev
Keyword(s):  
Linear Method ◽  
Super Resolution ◽  
Local Linear ◽  
Local Linear Method

Local-linear method of super-resolution for compensation of image distortions using new model of turbulence

2004 ◽  
Author(s):  
Fedor V. Shugaev ◽  
Evgeni N. Terentiev ◽  
Ludmila S. Shtemenko ◽  
Olga I. Dokukina ◽  
Oksana A. Ignateva
Keyword(s):  
Linear Method ◽  
Super Resolution ◽  
New Model ◽  
Local Linear ◽  
Local Linear Method

REWEIGHTED FUNCTIONAL ESTIMATION OF DIFFUSION MODELS

2009 ◽  
Vol 26 (2) ◽  
pp. 541-563 ◽  
Author(s):  
Ke-Li Xu
Keyword(s):  
Linear Method ◽  
Estimation Method ◽  
Diffusion Models ◽  
Linear Estimator ◽  
Limit Theory ◽  
Functional Estimation ◽  
Finite Samples ◽  
Negative Results ◽  
Local Linear ◽  
Local Linear Method

The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

THE CLUSNET ALGORITHM AND TIME SERIES PREDICTION

1993 ◽  
Vol 04 (03) ◽  
pp. 247-255 ◽  
Author(s):  
W. HSU ◽  
L. S. HSU ◽  
M. F. TENORIO
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Network Architecture ◽  
Time Series Prediction ◽  
Clustering Algorithms ◽  
Linear Method ◽  
Trade Offs ◽  
Local Linear Method ◽  
On Line ◽  
On Line Learning

This paper describes a novel neural network architecture named ClusNet. This network is designed to study the trade-offs between the simplicity of instance-based methods and the accuracy of the more computational intensive learning methods. The features that make this network different from existing learning algorithms are outlined. A simple proof of convergence of the ClusNet algorithm is given. Experimental results showing the convergence of the algorithm on a specific problem is also presented. In this paper, ClusNet is applied to predict the temporal continuation of the Mackey–Glass chaotic time series. A comparison between the results obtained with ClusNet and other neural network algorithms is made. For example, ClusNet requires one-tenth the computing resources of the instance-based local linear method for this application while achieving comparable accuracy in this task. The sensitivity of ClusNet prediction accuracies on specific clustering algorithms is examined for an application. The simplicity and fast convergence of ClusNet makes it ideal as a rapid prototyping tool for applications where on-line learning is required.

scholarly journals Evaluation and Numerical Simulation of Music Education Informationization Based on the Local Linear Regression Method

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jiping Liu
Keyword(s):  
Linear Regression ◽  
Convergence Rate ◽  
Music Education ◽  
Linear Method ◽  
Estimation Methods ◽  
Linear Regression Method ◽  
Theoretical Problem ◽  
Local Linear ◽  
Functional Components ◽  
Functional Linear Regression

The study of this theoretical problem enables sparse or dense functional data, including educational information evaluation data. The choice of different weights is subjected to principal component analysis. The evaluation of music education informatization level mainly evaluates the status quo of music education informatization development, provides a basis for formulating and adjusting music education informatization development policies, and provides support for educational decision-making, to promote the sustainable and balanced development of music education informatization. The evaluation of music education informatization has become the key promotion work of music education informatization at this stage. This paper studies the convergence rate of functional principal components based on the local linear method under general weighting conditions. First, we introduce the related research on the estimation of mean and covariance function under general weighting. Secondly, for principal functional components under general weighting, namely, eigenvalues and eigen functions, the text gives the corresponding estimated values and derives its strong uniform convergence rate. Finally, the convergence rate was verified by simulation research. The estimation methods and conclusions of this article enrich the research of functional linear regression models and will help analyze the complex and changeable problems encountered in the application of music education information.

scholarly journals Semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices

2021 ◽  
Author(s):  
Hongxia Wang ◽  
Xuehong Luo ◽  
Long Ling
Keyword(s):  
Convergence Rates ◽  
Least Squares Method ◽  
Linear Method ◽  
Trend Function ◽  
Autoregressive Coefficient ◽  
New Class ◽  
Temporal Models ◽  
Local Linear Method ◽  
Spatio Temporal ◽  
Better Than

We consider a new class of semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a type of sparse structure in order to include as many panels as possible. We apply the local linear method and least squares method for Yule-Walker equation to estimate trend function and spatio-temporal autoregressive coefficient matrices respectively. We also balance the over-determined and under-determined phenomena in part by adjusting the order of extracting sample information. Both the asymptotic normality and convergence rates of the proposed estimators are established. The proposed methods are further illustrated using both simulation and case studies, the results also show that our estimator is stable among different sample size, and it performs better than the traditional method with known spatial weight matrices.

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