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Full-Text Articles in Physical Sciences and Mathematics
Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu
Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu
Leming Qu
Statistical and machine learning is a fundamental task in sensor networks. Real world data almost always exhibit dependence among different features. Copulas are full measures of statistical dependence among random variables. Estimating the underlying copula density function from distributed data is an important aspect of statistical learning in sensor networks. With limited communication capacities or privacy concerns, centralization of the data is often impossible. By only collecting the ranks of the data observed by different sensors, we estimate and evaluate the copula density on an equally spaced grid after binning the standardized ranks at the fusion center. Without assuming any …
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 …
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.