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Full-Text Articles in Physical Sciences and Mathematics
Wavelet Thresholding In Partially Linear Models: A Computation And Simulation, Leming Qu
Wavelet Thresholding In Partially Linear Models: A Computation And Simulation, Leming Qu
Leming Qu
Partially linear models have a linear part as in the linear regression and a non-linear part similar to that in the non-parametric regression. The estimates in Partially Linear Models have been studied previously using traditional smoothing methods such as smoothing spline, kernel and piecewise polynomial smoothers. In this paper, a wavelet thresholding method for estimating the corresponding parameters in Partially Linear Models is presented. Extensive simulation results shows that wavelet smoothing approach is comparable to traditional smoothing methods when their assumptions are satisfied. But wavelet smoothing is often superior when assumptions about the smoothness of the underlying function of non-parametric …
Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu
Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu
Leming Qu
A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the WinBUGS software package.
Wavelet Image Restoration And Regularization Parameters Selection, Leming Qu
Wavelet Image Restoration And Regularization Parameters Selection, Leming Qu
Leming Qu
For the restoration of an image based on its noisy distorted observations, we propose wavelet domain restoration by scale-dependent ∫1 penalized regularization method (WaveRSL1). The data adaptive choice of the regularization parameters is based on the Akaike Information Criterion (AIC) and the degrees of freedom (df) is estimated by the number of nonzero elements in the solution. Experiments on some commonly used testing images illustrate that the proposed method possesses good empirical properties.
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Leming Qu
For the reconstruction of a nonuniformly sampled signal based on its noisy observations, we propose a level dependent l1 penalized wavelet reconstruction method. The LARS/Lasso algorithm is applied to solve the Lasso problem. The data adaptive choice of the regularization parameters is based on the AIC and the degrees of freedom is estimated by the number of nonzero elements in the Lasso solution. Simulation results conducted on some commonly used 1_D test signals illustrate that the proposed method possesses good empirical properties.