5,728 research outputs found
Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study
Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced
Adaptive Reduced Rank Regression
We study the low rank regression problem , where and are and dimensional
vectors respectively. We consider the extreme high-dimensional setting where
the number of observations is less than . Existing algorithms
are designed for settings where is typically as large as
. This work provides an efficient algorithm which
only involves two SVD, and establishes statistical guarantees on its
performance. The algorithm decouples the problem by first estimating the
precision matrix of the features, and then solving the matrix denoising
problem. To complement the upper bound, we introduce new techniques for
establishing lower bounds on the performance of any algorithm for this problem.
Our preliminary experiments confirm that our algorithm often out-performs
existing baselines, and is always at least competitive.Comment: 40 page
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